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Some implications of the experience factor for managerial accounting

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Some implications of the experience factor for managerial accounting
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Managerial accounting
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Bhada, Yezdi Khurshed, 1940-
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1968
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viii, 295 leaves : illus. ; 28 cm.

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Accountancy ( jstor )
Airframes ( jstor )
Capital costs ( jstor )
Cumulativity ( jstor )
Direct labor costs ( jstor )
Labor costs ( jstor )
Learning curves ( jstor )
Mathematics ( jstor )
Production costs ( jstor )
Unit costs ( jstor )
Accounting ( lcsh )
Accounting thesis Ph. D ( lcsh )
Dissertations, Academic -- Accounting -- UF ( lcsh )
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Thesis - University of Florida.
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Bibliography: leaves 284-294.
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Manuscript copy.
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Vita.

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SOME IMPLICATIONS OF THE EXPERIENCE
FACTOR FOR MANAGERIAL ACCOUNTING













By
YEZDI BHADA














A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY


UNIVERSITY OF FLORIDA
1968










ACKNOWLEDGMENTS


The author wishes to express his indebtedness to all those who

have assisted him in achieving his goals, including his supervisory

committee members: Dr. John 11. James, Dr. Ralph H. Blodgett, Dr.

Charles W. Fristoe, and Dr. Williard E. Stone. He is especially grate-

ful to Dr. James W. Davault, committee chairman, whose patience and

guidance were most encouraging. Gratitude must also be expressed to

Dr. Harvey E. Donley, Professor of Accounting, Bowling Green State

University, for his role in getting the author interested in the sub-

ject of this dissertation. Above all, he would like to express his

gratitude to his wonderful wife, Perviz, who preferred to sacrifice a

life of security and comfort to follow the man in whom she had faith.

Patiently has she endured years of hardship and loneliness, an accom-

plishment for which he bows his head in true respect.

Finally, he wishes to express his admiration for this wonderful

land of opportunity. God bless America, and all those who have made it

the great nation it is.











TABLE OF CONTENTS


ACKNOWLEDGMENTS . . . . . . . . . . . . .

LIST OF TABLES . . . . . . . . . . . . .

LIST OF FIGURES . . . . . . . . . . ... .

CHAPTER
I INTRODUCTION .. . . . . ..........

Nature and Scope of the Study .. . . ......
Definitions of Key Terms .. . . . ......
Research Methodology Employed .. . . ......
Organization of the Remainder of This Study .. ..

II EXPRESSING THE DYNAMIC RELATIONSHIP BETWEEN COST OR
PRODUCTION TIME AND THE QUANTITY PRODUCED .. . ...

Purpose and Organization of the Chapter .. . ...
A Historical Sketch of Contributions to the Estab-
lishment of a Cost-Quantity Relationship ......
Development of the Linear Logarithmic Dynamic
Cost Function . . . . . . . . . .
The Learning Curve .. . . . ........
A Critique of the Conceptual Implications of
Experience Curve "Theories" .. . . ......

III PROJECTING DYNAMIC PRODUCTION DATA .. . . ....

Purpose and Organization of the Chapter .. . ...
Accumulation of Accounting Data .. . . .....
Possible Patterns in Dynamic Production Data
Projections ....................
Variations Suggested for the Study of Dynamic Data.

IV QUANTITATIVE AND QUALITATIVE IMPLICATIONS OF THE
EXPERIENCE RATE . . . . . . . . . .

The Purpose and Organization of the Chapter .. ..
Statistical and Mathematical Implications .. ...
The Experience Rate and the Slope of the Experience
Curve . . . . . . . . . . . .
Significance of the Experience Rate .. . ....
Factors Influencing the Experience Rate .. . ...

V SPECIFIC IMPLICATIONS FOR MANAGERIAL ACCOUNTING ..










TABLE OF CONTENTS (continued)


V The Purpose and Organization of the Chapter .... 192
Implications for Costing. . . . . . . ... 193
Implications for Planning . . . . . . . 215
Implications for Control. . . . . . . ... 234

VI SUMMARY AND CONCLUSIONS .. . . . . . . 262

APPENDICES
A OTHER TERMS USED IN PLACE OF, OR IN REFERENCE TO,
THE EXPERIENCE CURVE. . . . . . . . ... 278

B UNIT HOUR FORMULA MODIFIED FOR DESIGN CHANGES AS
SUGGESTED BY GARG AND MILLIMAN. . . . . . ... 280

C DERIVING THE LOCARITHMIC LINE OF BEST FIT USING THE
METHOD OF LEAST SQUARES . . . . . . . . 281

BIBLIOGRAPHY ............ . . . . . . ... 284

BIOGRAPHICAL SKETCH .................. . . 295










LIST OF TABLES

TABLE PAGE

II-I Selected Values from an Hypothetical Cumulative
Production Schedule. . . . . . . . ... 55

II-II Selected Cost Data for Product X. . . . . ... 67

II-III Cost Data Signifying Constant Rate of Decline for
Tripled Quantities . . . . . . . . . 74

III-I Production Data Indicating a Constant Rate of Improve-
ment for Unit Hours . . . . . . . ... 98

III-II Production Data Indicating an Initially Fast Rate of
Improvement for Unit Hours. . . . . . . ... 101

III-III Production Data for Units Produced in Identifiable
Lots. . . . . . . . . .. ...... 106

III-IV Production Data Indicating a Constant Rate of Improve-
ment for Equal Quantities Produced. . . . . ... 115

III-V Production Data Indicating No Apparent Trend, Before
and After Reclassification. . . . . . . ... 125

IV-I Assembly-Time Analysis for the First Nineteen Units
Produced. ... . . . . . . .. ... 142

IV-II Assembly-Time Analysis for the Next Twenty-Five Units
Produced. ... . . . . . . .. ... 151

IV-III Slope Coefficients, Conversion Factors, and Angles
of Decline, for a Range of Experience Rates . . .. .166

IV-IV Relationship Between Manual-Mechanical Ratios and
Experience Rates for Four Industries. . . . . 174

IV-V Relationship Between Manual-Mechanical Ratios and
Their Corresponding Experience Rates for Various
Operations ............ .... .. . 174

V-I The Effect of Declining Cost Per Unit on Resultant
Profit. ... . . . . . . . .... 205

V-II Production Cost Analysis with and without Consideration
Given to the Experience Factor. . . . . . ... 212

V-III Relationship Between Increases in Quantatives Ordered
and Their Resultant Prices. . . . . . . ... 228

v










LIST OF FIGURES


FIGURE PAGE

I-1 Long Run Production Time Declines Experienced in
Two Industries. . . . . . . . ... .. 6

II-1 Representative "Learning Curves" As Used for Psycho-
logical Analyses ................... 49

II-2 An Actual Learning Curve Derived in a Psychological
Experiment ....... ... ............ 51

11-3 An Example of a "Learning Curve" Used for an Incentive
Wage Payment Scheme . . . . . . . .. 52

11-4 Graphical Representation of Initial Cumulative Produc-
tion Data on Arithmetic-Grids . . . . . ... 56

11-5 Graphical Representation on Arithmetic-Grids After a
Substantial Level of Production Has Been Achieved . 58

II-6 Hypothetical Data (from Table 1) Plotted on Logarith-
mic-Grid Graph Paper. . . . . . . . ... 60

11-7 Effect of Different Improvement Rates for Cost Elements
on the Total Cost Projection . . . . . . 69

II-8 Effect of Linear Component Curves of Different Slopes
on the Unit Curve . . . . . . . . ... 71

II-9 Constant Rate of Decline for Tripled Quantities As
Projected on Logarithmic-Grids. . . . . . ... 75

III-1 Constant Rate of Decline for Unit Labor Hours .... 99

III-2 Constant Rate of Decline for the Cumulative Average. 103

III-3 A "Scalloped" Representation. . . . . . . .107

III-4 Constant Rate of Decline for Lot Averages . . ... 108

III-5 A Humped Unit Hour Curve. . . . . . . 110

III-6 An "Inverted S" Curve ... . . . . . 113

III-7 Constant Rate of Decline for Equal Quantities,
Projected on Full-Logarithmic Grids . . . ... .117











LIST OF FIGURES (Continued)

FIGURE PAGE

III-8 Constant Rate of Decline for Equal Quantities,
Projected on Semi-Logarithmic Grids . . . ... 118

III-9 An Example of a "Leveling-Off" Curve: Lockheed,
Burbank--B 17 . . . . . . . . . 120

III-10 An Example of a "Toe-Up" Curve: Boeing Seattle,
B 17 Learning Curve . . . . . . . ... .121

III-11 An Example of a "Toe-Down" Curve: Douglas, Tulsa
B 24 Learning Curve . . . . . . . ... 123

III-12 A No-Trend Projection ..... . . . . .126

III-13 Trend-Lines from Reclassified No-Trend Data . . .. .127

IV-1 Unit Hours from Table IV-1 Plotted on Arithmetic
Grid Graph Paper .................... 144

IV-2 Unit Hours from Table IV-1 Plotted on Logarithmic Grid
Graph Paper . . . . . . . . ... . . 145

IV-3 "Raw" Trend on Logarithmic Grids. . . . . ... 146

IV-4 A Linear Function Fitted to the Data from Table IV-1. 147

IV-5 A Third Degree Polynomial Fitted to the Data from
Table IV- . . . . . . . . . . . ... 149

IV-6 Figures IV-4 Replotted with Data from Table IV-II
Added to the Original Graph . . . . . ... .152

IV-7 Straight Line Projections Using Different Points
for Derivation of Trends. . . . . . . ... 153

IV-8 Straight Line Projections Using Different Points for
Derivation of Trends, As Applied to the Cumulative
Average Plots ......... ........... .. 155

IV-9 Extrapolations of Trends Indicated in Figure IV-8
for Large Quantities. . . . . . . . ... 157

IV-10 Unit Hours from Tables IV-I and IV-II Plotted on Plain
Graph Paper with Trends Indicated Using Polynomials . 158










LIST OF FIGURES (Continued)

FIGURE PAGE

IV-11 Trends Fitted to Satisfy One Version of the
"Experience Curve Theory" . . . . . .... . 161

IV-12 Trends Fitted to Satisfy the Other Version of the
"Experience Curve Theory" . . . . . . .. .162

IV-13 Derivation of the Slope Coefficient . . . . . 164

V-1 Comparison of Break-Even Points . . . . ... .214

V-2 Usage of Constant Times, Compared with Declining Time
Per Unit for Labor Requirement Forecasting. . . ... 219

V-3 Comparing Effectiveness of Two Control Lines on a Set
of Data Plotted on Plain Graph Paper. . . . ... 238

V-4 Comparing Effectiveness of Two Control Lines on a Set
of Data Plotted on Logarithmic Grid Graph Paper . . 239

V-5 An Example of Control Through the Use of Declining
Trends. . . . . . . . . .. .... 242

V-6 An Example of Control with the Aid of Confidence Limits. 245

V-7 Effect of Declining Production Time on Variance
Analysis ........... ... ......... 250

V-8 Influence of Worker-Learning on Productivity. ... .256











CHAPTER I

INTRODUCTION


The purpose of this chapter is to give the reader an idea regard-

ing the subject matter of the study. Specifically, to express the nature

and limitations of the work undertaken, to state the involved hypotheses,

to define certain key terms, to throw light on the methodology used, and

to outline the study in general.

Special care has been taken to substantiate assumptions accepted,

and to differentiate the work undertaken by this study from apparently

similar research conducted under the aegis of various disciplines. That

the study has been made from a managerial accountant's point of view has

been emphasized, and a generalized indication of what this involves has

been attempted.


Nature and Scope of the Study

Recognition of the phenomenon of experience

The hypothesis that an organism improves its effectiveness, or,

in other words, "progresses," may be validated without detailed investi-

gation by means of everyday observations, or with the help of simple

scientifically controlled experiments. Those who appreciate a less

rigorous approach might be tempted to consider the hypothesis as "evi-

dent," on the ground that one improves as one partakes in the events of

existence; and given a sufficient period of time, one is bound to become

more efficient, especially in cases which involve repetitive operations.












For the purpose of research, the above hypo -s ; has been ac

cepted, but not on a priori grounds. Several studies have bt: T. ,

ranging from experimentation with individuals as subjects under simulated

conditions, to ex-post observations involving entire industries function-

ing under normal conditions. Almost all the references listed in the

bibliography substantiate the hypothesis in one way or another. However,

an investigation might be in order.

Historical data furnish a reliable starting point to serve as evi-
1
dence of the existence of improvement as a product of experience. The

human race has come a long way since the time man sustained his physio-

logical needs by trying to kill his animal adversaries with the help of

bare hands. It was not long before man "learned" that the task could be

accomplished much more efficiently by creating special equipment. He

even found that he could optimize his situation by bartering his surpluses

in order to receive scarce goods in return. With time he learned to do

several new operations and to perform various functions more efficiently,

until finally he arrived into the age of trade and commerce, and was soon

engulfed by the industrial revolution.

The need for increased production led to the introduction of more

efficient capital equipment, and the rate at which obsolescence began to

be recognized for otherwise productive equipment was continuously increas-

ing. In other words, man was developing his effectiveness through the

experience he had gained in the process of living. Even the tenets of

"scientific management" ushered in by Frederick Taylor and others depended

to a considerable degree on the implied assumption of "experience" and












improvement. Today, more than ever before, increases in productiveness

and efficiency can be witnessed in almost every walk of life, and the age

old adage "experience is the best teacher" is as widely accepted today as

it was several decades ago.

The causes of improvements, and the reasons for the existence of

experience, are varied. Several psychological theories have been formu-

lated, each of which may be questionable as to its assumptions, implica-

tions, and solutions. However, there can be little disagreement regarding

the acceptance of improvement as a phenomenon which can be witnessed, and

which can considerably influence life on our planet. There might be a

question of degree involved, for in some cases there might be more oppor-

tunities for improvement than in others; however, it can be safely

generalized that, given sufficient time, experience will affect efficiency.

Can we extend the above hypothesis regarding the phenomenon of

experience to business and industrial situations? The answer is an em-

phatic affirmative. There are several reasons for accepting the applica-

bility of the hypothesis to manufacturing situations. In the first place,

there would be the added factor of a concerted effort toward greater ef-

ficiency due to the element of competition in the business world. This

statement can again be validated by observing existential data. Micro-

economic theory implies an assumption, which can be used to support the

contention that in a competitive economy there has to be a tendency to-

ward optimization of efficiency, otherwise competition may force the firm,

or even the industry, out of business.

Moreover, production generally involves repetitive operations, and










one may be safe in generalizing that there is ample opportunity for

gaining experience at performing a function more efficiently. Under

such conditions the probability of grasping operations in terms of their

essentials is certainly high; and improvement through experience gained

is more likely.

As stated earlier, to verify the applicability of the hypothesis

to business situations, one merely has to collect the necessary data for

a product, process, firm, industry, or even an economy. Almost all refer-

ences cited in the bibliography involve some element of empirical investi-

gation to support the hypothesis. To illustrate, a few selected studies

are mentioned below.

A team of researchers at the University of Iowa investigated the

effect of learning on individuals at performing a punch-press operation

under laboratory conditions.2 The task was broken down into several sub-

operations (referred to as "therbligs"), and the effect of work-repeti-

tion on each of the therbligs was also studied. The results indicated

that although the rates of learning differed between individuals, and even

between different therbligs for the same individuals, there was a marked

learning pattern for each operator for the task as a whole. A number of

such simulated studies have been undertaken at universities and research

foundations, mainly conducted to aid psychological experiments, most of

which conclude with identical results.

Several citations can be made for experience affecting the produc-

tion of individual products, processes, and firms. For example, Werner Z.

Hirsch investigated the effects of the experience factor on eight products











3
and found a rate of improvement in all cases. In an article published

in another journal, Hirsch states: "Concerning the direction of the

slopes [of his plotted data] great consistency in the results was revealed.

In all cases the progress function had a significantly negative slope."

Other studies, taking into consideration entire industries, may be

noted. The Monthly Labor Review published a study undertaken by Allen D.
5
Searle to investigate production patterns in the shipbuilding industry.

In this study, it was observed that man hours required declined for subse-

quent production of similar ships, in individual yards, and for the indus-

try as a whole. In a similar type of study in the airframe industry,

almost identical results were observed.6

Some rather interesting examples have been cited by Winfred B.

Hirs-hmann on the long-term effects of improvement in specific industries.7

Figure 1 indicates the effect of continuous production on two major U. S.

industries: petroleum and basic steel. Similar patterns could be derived

for several other industries such as automobile, electric power, airframe

manufacture, and building construction. One might even generalize that

if data were properly adjusted, similar patterns might be observed for

any and every type of production facility.

One has merely to consider the regulations imposed by various

governmental agencies and other organizations regarding the utilization of

the concept to realize that not only is it recognized, but it is considered

extremely valuable. For example, the National Aeronautics and Space Ad-

ministration makes it obligatory for a contractor to consider the effect

of experience for reporting costs. A handbook has also been issued by









Per Barrel Refined in the Petroleum Industry

1888










S1962





I 1 1 I i tI I 1 I I I' ll I I I I i IlII

3 4 5 1,000 2 3 4 5 6 810,000 2 3 4 5 68 100,000
Cumulative Barrels ( In Millions )


Man-Hours


4.0


3.0


1 2.0


1.5 k


Per Unit of Output in U.S. Basic Steel Industry


500 1,000 1,500 2,000 3,000 4,000
Cumulative Units
Figure 1-1
Long Run Production Time Declines Experienced in Two Industries
'~*~""'"' """ "" """~" ~ ... ..... .. .., '~"


* 1920


S1925
** 1931
.* 5*
*


1940


"* 1950


,* ..
.*












NASA which presents guidelines and instructions for preparing necessary

forms, including Form 534a, on the preparation of the "Contract Progress

Curve Report."9 The General Accounting Office, the Defence Contract

Audit Agency, etc., have also issued detailed instructions on the usage

and implications of the experience factor.10

In conclusion, it may be reiterated that experience does affect

operations; and although the rate at which it affects different functions

may vary, its extence can be validated without serious difficulty.


Experience as studied by various disciplines

Philosophers, psychologists, management scientists, economists,

engineers, and others have all faced the implications of experience upon

their particular areas of interest. Undoubtedly, each discipline has

looked upon the significance of experience from its own subject-matter

point of view, and each has tried to answer different questions. It

might be pertinent to review briefly the types of questions posed, and

answers sought by each of these disciplines.

If one were to ask the question "what is philosophy," a variety

of replies might ensue, with perhaps no two answers being the same.

Professor Levi indicates that, at the very most, one could say, "It is

the activity of serious and able men reflecting upon, meditating, reason-

ing about, and considering deeply the nature of their experience. .

All philosophy begins with experience."

In other words philosophy has no subject matter of its own, but

draws its material from experience itself. It tries to formulate theories

which can be processed to enhance human understanding and knowledge which












could then be utilized for ordering human life in a more efficient manner.

The interest of philosophers is centered around experience as it affects

human existence, and not minor events.

Different philosophers have arrived at different conclusions de-

pending upon their particular points of view. Thus, the empiricists such

as John Locke, A. J. Ayer, and Bertrand Russell have considered the impli-

cations of experience differently than have the pragmatists such as John

Dewey, Charles Pierce, and P. W. Bridgeman. An investigation into the de-

tails of various views presented by the philosophers would be a digression

beyond the scope of this study, and hence it may suffice to say that the

study of experience as undertaken by students of philosophy may be con-

sidered as being of a different nature and scope than that undertaken in

this research.12

The amount of research done by psychologists in the area of learn-

ing needs little introduction. The main questions posed by the psycholo-

gists are: "Why does learning take place? How do people learn? and

what can be done to improve the rate of learning in individuals?" They

have long recognized that modes of perceiving are functions of past ex-

perience, which is another way of saying that they are products of learn-

ing; and knowledge of the characteristics and the conditions which deter-

mine the occurrence of learning is fundamental to an understanding of

psychological development and organization.13

The first two paragraphs from ProfessorsHilgard and Bowers' book

on the Theories of Learning are interesting enough to be quoted in full:











The study of learning is shared by many disciplines. Physi-
ologists, biochemists, and biophysicists have a legitimate
interest in it; parents, teachers, industrial managers, re-
habilitation workers, and others faced by the practical prob-
lems of the control of learning have their own needs which
require that they understand the basic processes and how to
manage them. Yet the scientific study of learning is car-
ried on primarily by psychologists. Psychology's claim to the
field was staked out in part by masterly pioneers such as Eb-
binghaus (1885) and Thorndike (1898). Those who have followed
in their footsteps have been primarily psychologists. Profes-
sional educators have welcomed educational psychology as a
foundation science upon which to build their practices, and
studies of learning have gone on concurrently in laboratories
of general psychology and laboratories of educational psychology,
with interplay between the pure and applied fields. Under the
circumstances, it is very natural for psychologists to feel
that the study of learning belongs to them.
In addition to historical reasons, there is another basis on
which to account for the psychologist's interest in learning.
This is the centrality of learning in the more general systems
of psychological theory. A scientist, along with the desire to
satisfy his curiosity about the facts of nature, has a predilec-
tion for ordering his facts into systems of laws and theories.
He is interested not only in verified facts and relationships,
but neat and parsimonious ways of summarizing these facts.
Psychologists with a penchant for systems find a theory of
learning essential because so much of man's diverse behavior
is the result of learning. If the rich diversity of behavior
is to understand in accordance with a few principles, it is
evident that some of these principles will have to do with the
way in which learning comes about.14

However, the psychologists' "claim to the field" has been mainly in

the area of trying to understand the reasons for the occurrence of learn-

ing, where and how it can be embodied, and finding ways and means of

stimulating the rate of learning. Above all, the science of psychology

deals primarily with the individual as a unit, and group behavior or

interactions encountered in business organization is beyond the scope of

its study.

Various theories have been offered as explanations for the existence

of learning. Hilgard and Bower supply a detailed reference to some of the











more important ones, including those of Edward L. Thorndike, Ivan Parloy,

Edwin R. Guthrie, B. F. Skinner, Clark L. Hill, Edward C. Tolman, Sigmund

Freud, and other prominent psychologists.15 For a more concise treatment,

the reader is referred to a series of three articles (of which Part I is

the most pertinent) by Roger Bellows.16

Once more, it can be reiterated that the problems of learning and

experience as viewed and investigated by the science of psychology are of

a significantly different nature than the problems as viewed and investi-

gated in this study. The differentiation is more clearly expressed further

on in this chapter.

A surprising amount of work has been done on the recognition of ex-

perience as a relevant phenomenon in the field of engineering, especially

in the area of industrial engineering. Yost of the early work on the ex-

perience factor was done by engineers, and the engineering departments of

various airframe production plants were the first to recognize and deal
17
effectively with the implications of experience. For example, T. P.

Wright, the father of dynamic cost relationship analysis, noted its im-

plications in his renowned article published in February, 1936, while

connected with the engineering function of Curtiss-Wright Corporation.18

As would be expected, the engineer is more concerned with the ef-

fects of experience on his specifications, production scheduling, etc.,

and any implications which do not involve his mathematical calculations

are disregarded as beyond the scope of his interest. Furthermore, most

engineering studies involve highly complicated mathematical treatments,

which may lie beyond the comprehension of other less sophisticated











personnel. However, the science of engineering has contributed consider-

ably to the proper measurement of experience, and has supplied tools for

measurements which were not otherwise available. Professor A. B. Berg-

hell's chapter on "learning curves" can still serve as an excellent refer-

ence for mathematical calculations regarding quantification of the experi-
19
ence factor.

It may be noted that there are several areas of similarity between

the nature of engineering studies and the work undertaken in this study;

however, the significant difference is in the scope of the studies. As

previously stated, the engineering studies are merely concerned with

specific applications to peculiar engineering models and problems. The

present study is more concerned with the implications from the standpoint

of managerial accounting. An excellent example of an engineer's interest

in the implications of experience is evidenced in a study made by Kenneth

Hammer for a thesis submitted to Cornell University as requirement for the

degree of Master of Science.20

Equally surprising is the allegation that not much work has been

done on the implications of experience in the field of economics.21

It should be noted that the experience factor (as defined later) is con-

cerned with what would be considered in economics as a "technological

change." Hence, in traditional micro-economic analysis, the factor is

assumed away in the construction of the static cost curves. The pro-

duction function, as derived with the help of actual data using cumu-

lative production and not rate of output, may be considered a dynamic

function, and hence cannot be compared to the traditional micro-economic












static cost model.

An attempt was made by W. Z. Hirch to reconcile the traditional

cost curves to the dynamic production functions obtained by using cumula-

tive production. The following quotation has been reproduced in order to

clarify any ambiguity that may exist regarding economic cost functions and

those derived during the course of this study:22

Most economic cost studies have been concerned primarily with
the relation of cost to rate of output. Shortrun costs are
usually said to be those associated with variation in the uti-
lization of fixed plant or other facilities, whereas longrun
cost emcompasses changes in the size and kind of plant. Strictly
then, the distinction is based upon the degree of adaptation of
all input factors to rate of output. However, cost may vary
because of changes in technical knowledge. Economists have
explicitly excluded all irreversible changes in technology.
Most longrun cost theories, for instance, are timeless; one
future point in time is selected at which output rate and
facilities are permitted to change. That such a cost func-
tion, particularly its height, will be affected by improvements
in technical knowledge is beyond doubt.
It is convenient to clarify the issue of the different cost
functions by referring to production functions, which express
the net relation between the input of variable productive fac-
tors and output curing a given production period, under the as-
sumption of a given plant and technical knowledge. From the
production function we can derive a static shortrun cost func-
tion which also assumes a given plant and technical knowledge.
Longrun cost permits changes in the size and kind of plant,
but assumes stability in technical knowledge. Thus, a longrun
cost function is related to points on different production
functions, each point involving a different plant while using
the same technical knowledge. There can be a cost function
which permits changes in technical knowledge but not in plant
and other facilities. In a sense this is a dynamic cost func-
tion. If direct labor is the cost we consider, we shall speak
about a (unit) learning of progress function. This expresses
the net relation between the amount of direct labor needed to
produce one product-unit and the cumulative units produced in
a given facility. The progress function thus permits us to
estimate the amount of direct labor needed to manufacture the
Nth unit, from N, the cumulative number of the product-unit.
The function is related to a number of points on different
production functions involving successive changes in techni-
cal knowledge in a given facility.











In a study conducted a few years back, Harold Asher bemoaned the

fact that hardly any consideration had been given to the implications of

volume on cost in economic literature, and stated that in the course of

his research only one pertinent reference was found, although he did con-
23
fess to a less than maximum attempt atlocating references.3 The last

decade or so has witnessed a few contributions, including those by Asher

and Hirsch, which were mentioned above. Noteworthy, among others, have

been those of Armen Alchian and Jack Hirshleifer. In a paper entitled

"Costs and Outputs," Alchian presented several propositions, including

one wherein he stressed the importance of anticipated volume along with

the rate of output for economic analyses.24 Alchian's comments insti-

gated Hirschleifer to continue research in the same direction, and the

results of his study were published by The Journal of Business.25

Hirshleifer's review and development of Alchian's conceptions are inter-

esting to note, for an attempt has been made to reconcile classical

economic theory with empirical observations. However, the temptation to

delve into the stated implications for economic analyses has been sub-

dued, for the topic is considered beyond the scope of the present study.

Another field (if one can refer to it as such) in which some work

has been accomplished regarding the implications of experience has been

that of operations research. However, the major portion of work done in

this area has been the adaptation of learning "theories" to business

problems. In other words, the focal point of interest has been "how

can the rate of learning be improved through providing incentives, etc."

A few studies have been directed toward other problems, which might be












considered in the realm of the accountant's interest, and these can be

considered in relation to the next section.

A few other disciplines, including business management, quantita-

tive analysis, markctin,', and purchasing have recognized the existence

of experience as a factor to be taken into consideration, but the ap-

proaches used in these cases have not been very much different from those

utilized by the field of accounting, as discussed in the next section.

Differences, if any, may be attributed to varied emphasis and scope

rather than the nature or subject-matter under investigation.


Experience as viewed by the managerial accountant

Who is a "managerial accountant?" Ihat is "management accounting?"

How does it differ from any other form of accounting? These and other

pertinent questions might have to be answered before one can digress into

further discussion on the subject for this section.

As this study is not on the finer points of management accounting,

it might be advisable to refer to some authority on the subject. A state-

ment prepared by the research staff for the guidance of members of the

committees on research planning and accounting development and issued by

the National Association of Accountants may be considered such an author-

ity. The Association has defined the term as accepted previously by the

Anglo American Council on Productivity:

Management Accountancy is the presentation of accounting
information in such a way as to assist management in the cre-
ation of policy and in the day-to-day operation of an under-
taking.
The technique of accountancy is of extreme importance
because it works in the most nearly universal medium available
for the expression of facts, so that facts of great diversity












can be represented in the same picture. It is not the
production of these pictures that is a function of manage-
ment, but the use of them.26

In other words,rmnagement or managerial accounting is that phase

of accounting which actively supplies cost and other financial informa-

tion to management for more efficient planning, organization, and control--

information relevant to "internal" matters which can help management in

its task of decision-making. Although emphasis is on information of a

quantitative nature, there are elements of qualitative judgment involved.

Thus, along with reporting of relevant data, there is the responsibility

for communication and interpretation of the results. In any management

function such as establishing objectives, planning, organizing, direct-

ing, staffing, controlling, the decision-maker can benefit from the data

provided by the management accountant.

The definition quoted above distinguishes managerial accounting

from "financial" accounting on the basis of active participation by the

management accountant in aiding decision-making of an internal nature. It

is not contended that managerial accounting is completely independent of

financial accounting, or vice versa. There is a marked relationship

between these areas; however, the differentiation is in the goals aimed

at, and the means available to attain the goals.

The managerial accountant can help in the function of planning by

furnishing relevant data for costing, pricing, budgeting, forecasting cash

and fund flows, determining proper product mixes, providing solutions to

operate-or-lease problems, expansion-or-shutdown situations, make-or-buy

decisions, capital investment decisions, and various other decisions











needing special information. Proper control can be accomplished by set-

ting proper job, or process, cost systems, by the setting of standards,

comparison of actual costs with set standards, and actual costs with

budgeted figures, analyzing variances, etc.27 In all these areas, the

accountant is interested in establishing as much accuracy in his report-

ing function as possible, taking cognizance of the constraints encoun-

tered in any particular situation. However, to formulate effective in-

formation, judgmental factors might be involved. This makes him depen-

dent to a considerable degree on statistical tools, such as the "average,"

extrapolation of data obtained from actual operations, and other tools

and methods normally used for planning and forecasting.

Now, if experience is involved in a manufacturing situation, then

it might affect the different tasks of costing, pricing, etc. and the

effect might be significant enough to introduce an element of ineffective-

ness in the task of the managerial accountant. For example, the cost of

direct material and direct labor is usually considered as fixed per unit

of product. Thus, if one finds the prime cost of unit A to be $5, the

prime cost of unit X is also assumed to be $5, irrespective of whether X

is the hundredth or the thousandth unit. However, if the experience fac-

tor is taken into consideration, it might be found that the prime cost of

unit X is not $5, but less. This might be due to the factor of experi-

ence causing a more efficient usage of materials and labor in subsequent

production, which in turn would lead to a lower cost per unit.

The significance of the deviation can be understood if one considers

the "average" prime cost as $5. In other words, all the hundred or thousand











units might be costed at $5 per unit, whereas the final units might actu-

ally have only $2 of prime cost embodied in them. The point is that ac-

counting calculations provide as accurate results as the statistical tools

and data applied, and inaccuracies in accumulation of classification, or

use of methods could generate significantly unreliable results.

In other words, if it is found that experience is a relevant factor

to be considered for managerial accounting purposes, the results obtained

by taking it into consideration would be more accurate than those obtained

when its implications are disregarded. Therefore, it can be stated that

the managerial accountant is interested in the experience factor inasmuch

as it affects his tools, techniques, methods, and concepts.

He is not interested in why human beings learn, or the reasons for

experience leading to improvement as the psychologist might be. Neither

is he interested in how to improve the rate of gaining experience among

individuals, other than how he can guide management in making decisions

in a manner that may produce optimization of efficiency. He is certainly

not interested in philosophizing regarding the production experience in a

manner by which the world would benefit intellectually through the gain-

ing of experience. (In a particularistic sense, he might be considered

as "philosophizing," although not in the sense of the generally accepted

meaning of philosophy.)

His interest in experience for engineering specifications and com-

plicated mathematical implications is purely incidental, and even if con-

sidered within his realm, would constitute only a minute area of interest.

His interest in the economics of technological change may be considered as












more akin to his own area; however, as the subject of the effect of ex-

perience on economic analysis deserves more attention than short com-

ments, it can be looked upon as a specialized area of study. Accordingly

it will be considered as beyond the scope of this research, not for reasons

of irrelevancy, but merely to keep the study within manageable bounds.

Again, the managerial accountant is interested in any phenomenon

only as it affects his analysis. This factor of relevancy would dictate

his interest in most matters connected with individual firms and their

specific products rather than entire industries or the economy as a whole.

For this reason, plus the fact that the study has to remain manageable,

primary interest has been related to a consideration of experience as it

affects products and firms, rather than long-run industry trends. In

other words, industry growth curves or economy-wide projections have been

considered beyond the scope of this study, and any comment in connection

with these areas have been clearly noted.

Similarly "learning patterns" among individuals or social groups,

other than their indirect effects on business decision-making, would also

have to be considered as beyond the scope of this study.

The managerial accountant is primarily concerned with answers to

questions such as:

1. How does the factor of experience affect managerial decisions?

2. tWat can be done to incorporate the effects of experience in
reporting to management? That is, how can these effects be
related to the various tools, techniques, and concepts so that
more reliable interpretations can be made from the data
available?

3. What are the best means by which the effects of experience can
be quantified and measured?











4. Are the results obtained from using such quantifications
more significant for management decision-making?

5. What are the limitations and dangers of the attempted in-
corporating of the effects of experience?

6. Are there generalizations which could be hypothesized? Or, on
the other hand, how important are the special conditions con-
nected with different situations?

In short, the managerial accountant is only interested in the fact

that experience does affect efficiency, which in turn affects his position

as a member of the management team. If the effect of experience is sig-

nificant, if it can be quantified or otherwise incorporated into his area,

he can utilize such information for aiding management in the functions of

planning, organizing, and control. He is not interested in the "theory

behind" its occurrence, but only whether the phenomenon can be observed,

quantified, and incorporated in his field for greater effectiveness in

facilitating business decision-making.


The purpose of the study

The purpose of this study is to investigate the implications of ex-

perience on the various managerial accounting tools, techniques, and con-

cepts. The intention is to determine the effects of experience, to find

means of incorporating such effects br accumulation, dissemination, inter-

pretation, and reporting of pertinent information to management for ef-

fective decision-making in the functions of planning, organizing, and

controlling.

Means of quantification and incorporation have been studied as to

their applications and limitations, and evidence to support particular

approaches sought. The task of the managerial accountant has been kept











uppermost in mind while suggesting means and approaches.

The effect of the experience factor on costing for manufacturing

costs, including material, labor, and overhead, and of marketing and

general administrative cost, has been looked into. Its effect on cost-

volume-profit relationships has been investigated. The setting of

standards and standard costs incorporating the experience factor has been

studied, and solutions for proper incorporation supplied.

In other words, it is the intention of this study to bring the

factor of experience to the attention of the accounting profession, which

has neglected its implications to a significant extent. The truth is that

one hardly finds any mention of the subject in conventional textbooks, and

very little effort has been made to consider its effects on problematic

accounting situations.

The purpose of this study is to show the accounting profession that

the experience factor can be quantified, that dynamic production data may

be applied for more effective quantitative analyses, and that the results

derived from taking the effect of continuous production into consideration

might contribute significantly to their function. In other words, it has

been indicated that it might not be advisable to disregard the implica-

tions of experience on judgments based on a priori assumption such as

"too difficult to apply," or "insignificant in our case," without actu-

ally making a concerted attempt to determine its effects.

Some tentative hypotheses of this study are:

I. Tit '*.pr-.rjinre is a factor which affects manufacturing situ-


2. That this factor can be quantified and incorporated into
accounting analysis;












3. That the incorporation might involve more than the over-
simplified linear logarithmic model popularized by the
learning curve theory;

4. That the effectiveness of managerial accounting can be
enhanced by considering the factor of improvement; and

5. That failure to investigate its implications might lead
to inaccurate and inefficient results of diminished value
to management.

It is not contended that the efficiency derived from incorporating

the experience factor will more than offset the effort expanded in all

possible cases, for only the criterion of relevancy can determine its

efficacy. However, it is contended that the use of accounting results,

where no attempt has been made to investigate the effects of experience,

may be liable to serious error. In other words, if care is taken to

introduce the factor of experience, and if the results obtained after

such an attempt do not lead to increased efficiency, then its effects

may be discounted. However, its implications should not be discounted

on a priori assumptions, for not much effort might be needed to study the

effects of experience in industrial situations.


Definitions of Key Terms

It might be advisable to attempt definitions for some of the

terminology utilized, for it has to be admitted that the key terms used

for the purpose of this study could lead to misunderstanding, if not

properly understood. The reason is evident; the terms might have several

accepted meanings, but might have been used in this study with special

connotations.











Experience and learning

The word "experience" has been used to denote the phenomenon of

gaining positive efficiency, observable in the form of quantitative im-

provement in the course of an operation being repeated over a period of

time. In other words, while performing a repetitive operation, if im-

provement can be witnessed, the factors which aggregatively contribute

to such improvement are collectively referred to as "experience."

In the generally accepted sense of the terms (as witnessed by

dictionary definitions), "learning" is contrasted to "experience" on the

grounds that the former is knowledge acquired through study or instruc-

tion, as compared to "experience," which is defined as knowledge gained

through actual performance of existential operations. This implies the

dichotomy found in the study of philosophy as propagated by the ration-

alists and the empiricists, respectively.

This distinction has not been accepted in the use of the terms.

Rather, the term experience has been used to denote an interplay of

existential and conceptual data which would be involved in the process

of pursuing the desired goals. In this sense, learning may be considered

synonymous to experience.

However, there is a slight differentiation between the terms as

used in this study. The term "learning" has been used more in reference

to the acquisition of knowledge on the part of an individual, as con-

trasted to the usage of the term "experience" which has been utilized to

refer to groups or organizations. As the study is concerned more with

firms and industries than with learning on the part of individuals, it












has been deemed advisable to use the term "experience" to designate the

phenomenon which leads to the quantitative improvement with the occurrence

of repetitive operations in industrial situations.

Reference to a repetitive event does not imply identical repeti-

tion, but merely one where there are points of similarity. Thus two

operations might be substantially dissimilar; and yet, the initial might

contribute some knowledge to a more efficient performance of the succeed-

ing operation.

To reiterate, the question regarding "why" human beings are sus-

ceptible to this phenomenon of experience is beyond the scope of the

study. That this phenomenon can be observed, quantified, and used ef-

fectively for decision-making purposes is of prime importance for the

research undertaken.


Experience durve

The function that results from plotting dynamic production data on

any graph paper has been called an experience curve. Such a curve may be

linear or non-linear, smooth or uneven, downward sloping, flat, or upward

sloping. This explanation of the experience curve differs from the more

generally accepted learning curve, which necessarily implies a downward

sloping smooth projection on logarithmic graph paper.28

However, it should be noted that there may be several types of ex-

perience curves; such as, the unit hour experience curve, the cumulative

average experience curve, the lot average experience curve, and the

cumulative total experience curve. Care should be taken to identify the











type of experience curve involved, for each of the four stated above have

different implications and uses.


Experience factor, experience rate, and the slope of the experience curve

The term experience factor is used to designate the existence of

experience in a particular situation. Thus, the reference is more to the

"factor of experience" or the "fact of experience," as witnessed in the

situation being discussed. This can be contrasted to the experience rate,

where a constant rate of improvement is involved. In this case, there is

a specific quantitative rate which can be observed, and it is not just the

general phemonenon of experience that is referred to.

Whereas the experience rate is mentioned as a constant percentage

decline in unit or cumulative average costs, labor hours, etc. for every

doubled quantity, the slope of the experience curve denotes the exponen-

tial coefficient of the curve for use in mathematical calculations. Thus

a 90 per cent cumulative average rate indicates that the cumulative costs

or cumulative labor hours decline by 10 per cent with every doubled pro-

duction. This 90 per cent rate may be represented on a downward sloping

cumulative average curve, the slope of which can be expressed by the co-

efficient 0.152.


Experience curve concept and experience curve technique

The experience curve concept refers to the conceptual implications

of the factor of experience on a generalized basis. In other words, the

entire notion of experience and its implications for business in general

are reflected upon.











On the other hand, the experience curve technique refers to the

specialized tool, commonly known as the "learning curve." Thus the

technique requires the proper utilization of data to derive the experi-

ence rate, and its application for decision-making purposes. The utili-

zation does not refer to any one specialized use but to its usage for

aiding the solution of any problem toward which it can supply relevant

data. If statistical or mathematical tools are employed for quantifying

data, such that the experience factor is taken into consideration, then

the experience curve technique has been employed.


Managerial accounting tools, techniques, and concepts

The three terms, tools, techniques, and concepts, aggregatively

represent conceptual and practical aids utilized by the discipline of

managerial accounting. In other words, it would be preferable to look

upon the three terms as a set constituting any means used by the field

for purposes of analyses rather than be reflected upon for their indivi-

dual characteristics.


Dynamic production data

The term "dynamic" implies a continuity of operations for a given

set of data. Hence the label "dynamic production data" refers to manu-

facturing information collected from continuous operations. This study

is interested in the effect of change through repetition of production,

therefore interest is centered on information which can separate the ef-

fect of acquired experience on production time and cost. The terms

dynamic, cost-quantity, production time-quantity, volume, continuous,











and repetitive production data or relationships have been used to refer

to the same thing, namely quantitative information about production situ-

ations where considerable quantities are involved.


Direct labor hours

These hours refer to men-hours rather than the group or plant

hours. Stated differently, a total of the hours worked by each indi-

vidual on the job as opposed to the time spent by a group as a unit is

referred to. For example, five workers assembling one unit in an eight-

hour day would be considered as utilizing a total of forty direct labor

hours for the unit assembled, rather than the eight hours collectively

worked on by the group.


Linear protection and the linear hypothesis

The linear projection refers to a smooth straight line on full

logarithmic graph paper rather than on arithmetic grid graph paper or a

semi-log graph paper, unless specifically stated. The linear hypothesis

has been used by this study in reference to the "theory" that dynamic

production data necessarily implies a constant rate of decline in costs

and production hours with a duplication in the number of units produced.

In other words, the linear hypothesis states that plotting dynamic data

on logarithmic grid graph paper results in a linear projection.


Research Methodology Employed

Reasons for rejecting a case study approach

It was the original intention of this study to undertake empirical

case studies involving a range of situations. However, this mode of











research was abandoned for several important reasons. In the first place,

several studies can be found which relate to practical examples of speci-

fic situations and which lend support to certain hypotheses as formulated

by the individual authors. Unfortunately, due to the constraints en-

countered in using a specific set of conditions as the basis for a study,

there has been a tendency to state particular findings as generalizations.

Most of the case studies indicate some form of applicability or the recog-

nition of the experience factor to the particular situation, and hence

are considerably limited in scope. This does not imply that the form of

study is valueless; as a matter of opinion, it has great value.

However, an undertaking of a detailed empirical investigation

would have seriously limited the scope and value of the present study,

for the author firmly believes that in order to conduct a reliable in-

vestigation, especially where internal financial information-gathering

is concerned, one has to be an integral part of the researched unit, and

the serious limitations encountered by an outside investigator might

significantly impair the efficacy of the results obtained. This can be

witnessed from considering the difficulties encountered by the author in

his attempts at securing appropriate information. A great deal of time

and trouble was expended in trying to get data on the American ship-

building industry. An initial investigation had revealed that data from

that industry could be particularly amenable for research purposes, es-

pecially since there were various sizes of shipyards which could be in-

vestigated. Unfortunately, a definite reluctance on the part of the

industry to furnish data for the research led to the abandonment of all












aspirations for an impirical investigation. Other attempts in this

direction were also made but had to be similarly abandoned.


The paucity of literature on the subject

A rather distinct pccularity encountered in the course of the re-

search was an apparent lack of relevant literature on the subject. The

Accountant's Index to Periodicals referred to approximately twenty refer-

ences over a period of almost half a century. The lack of literature was

not quantitative in nature as it was qualitative, for a majority of the

references were simplified recapitulations of the learning curve theory

and its applications. Considerable effort was expended to secure and

review all available literature, and if any work was overlooked it was

either because of its unavailability, or that its existence was unas-

certainable despite all possible efforts. It may be asserted that the

bibliography prepared by the study is perhaps the most comprehensive

available on the subject.


The approach used

Under the above-stated conditions, it was decided to rely, to a

considerable degree, on the researcher's own experience and knowledge of

the subject gained over a period of years. This knowledge, along with

the available literature (including the case studies), has been utilized

to investigate the subject. The emphasis has been on experimentation at

the conceptual level, using existential data wherever appropriate. By

"experimentation at the conceptual level" is meant the study of the im-

plications using hypothetical data which could be adjusted to observe












variations and effects on different situations. Wherever data from actual

situations were available, such data were used in place of the hypotheti-

cal examples.

In the derivation of the experience factor, statistical and mathe-

matical means have been utilized, but not without proper care to under-

stand their implications and limitations. The acceptance or rejection of

otherwise non-substantiated assertions has been accomplished using the

author's own experience and knowledge as the criterion.

The remainder of the study has been conducted using conventional

management accounting tools, techniques, and concepts, and introducing

the element of experience to see the effect on the problem at hand.

Thus, regular situations have been taken, the element of experience intro-

duced into the situation, and the resultant conditions observed, with the

degree of variations being noted. Solutions to the problems created by

the added factor have also been sought and tested, wherever feasible.

It is honestly believed that the advantages obtained by the use

of hypothetical figures through a greater degree of maleability have

more than offset the disadvantages encountered from not using actual

data for validating hypotheses.


Organization of the Remainder of This Study

Since the subject matter of this study has been given considera-

tion by various individuals and firms, it has been deemed necessary to

undertake a historical review of the work done in the area. Such a task

has been undertaken in Chapter II. Only a few important contributions











have been briefly discussed, for other studies have done adequate tasks

on historical reconstructions which can be referred to for further detail.

The development of dynamic cost data for management usage has also been

traced as part of the historical review. After distinguishing between

"learning curves" as used for different purposes, a detailed critique

of the business "experience curve" has been undertaken to point out its

assumptions, characteristics, and general implications.

Having pointed out the implications of the experience curve

"theories," the role of the accountant as the person responsible for the

collection of data which can be used for aiding management decisions has

been probed. The task of recording, accumulating, and classifying produc-

tion data which can aid quantification of the experience factor requires

special emphasis and procedures which might differ from conventional

methods. These differences are analyzed and enumerated. Furthermore,

an important function performed by the accountant, namely interpreta-

tion of the data gathered, needs special emphasis and understanding,much

more than a casual knowledge of the learning curve "theory" can supply.

This task of interpretation can be efficiently undertaken only if

one is aware of the various patterns and trends continuous production

data can take. To give an idea regarding possible trends, a major por-

tion of Chapter III has been devoted to explaining and illustrating dif-

ferent patterns observed in actual situations or under experimental con-

ditions. Variations on the study of dynamic production data have also

been explained in this chapter.

That statistical and mathematical tools are involved in the study












of dynamic relationships is a point hardly ever mentioned in accounting

literature. In order for the analysis to be properly executed, some

knowledge of the implications of these quantification tools would be

necessary. For example, logarithmic graph paper can be used in place

of plain arithmetic graph paper for plotting trends, provided the set

of data can be expressed by the mathematical formula Y = axb. If this

formula does not provide the best fit, the arithmetic grid graph paper

might prove more beneficial. The point is that an unconditional usage

of the logarithmic graph, as proposed by literature, may prove less ef-

ficient under certain conditions. Hence, statistical and mathematical

implications have to be recognized, and Chapter IV has undertaken the

charge of expressing their involvement. To aid analysis, a set of data

collected in an actual manufacturing situation has been used, not to sub-

stantiate any generalized hypothesis, but merely for convenient illustra-

tion.

A differentiation between the experiencerate and the slope of the

experience curve has also been attempted in that chapter. The mathemati-

cal quantifications demonstrated have been deemed important as aids for

analyzing trends and qualitative judgments to be used in decision making.

The significance of the experience rate for interpretation purposes has

then been analyzed, leading to a rather important consideration of the

factors that affect the experience rate. Although an interdisciplinary

approach would be necessary for proper research into the factors that

contribute to the rate of improvement, an attempt has been made to

enumerate pre-production and during-production factors. It is hoped











that a framework for future research has been indicated for investigation

of the factors that contribute to a decline in manufacturing time with

increased quantities produced.

Implications of the experience factor for specific tools, techni-

ques, procedures, etc. have been investigated in Chapter V, where an ar-

bitrary classification has been used for purposes of analysis. Thus,

particular effects for costing of materials, labor, manufacturing over-

head, distribution expenses, and administrative expenses, for ascertain-

ing unit costs and profits, for evaluating and forecasting inventories,

and implications for the division of costs into their fixed and variable

element have been analyzed under the section on costing. Forecasting

labor requirements, setting wage incentive schemes, budgeting, pricing,

and selecting between alternatives, such as make-or-buy, constitute some

of the more important subjects investigated under the section devoted to

planning implications. Cost control, how it is affected by the factor of

experience, and how this factor could be incorporated for better analysis

have been viewed in the section on control implications, where control

charts, standard costing procedures, design change measurements, and

other less celebrated control aids have been selected for discussion.

The final chapter has been devoted to an enumeration of the con-

clusions reached in the course of the study. It also contains a note on

the possible avenues for future research in the area, research that could

conceivably prove fruitful.











-PG6NOTES
Cha pter I


1. For definitions of some terms used in this report see pp. 21-26.

2. R. M. Barnes, J. S. Perkins, and J. M. Juran, "A Study of the
Effects of Practice on the Elements of a Factory Operation," University of
Iowa Studies in Engineering, Bulletin 22 (November, 1940), pp. 3-86.

3. W. Z. Hirsch, "Manufacturing Progress Functions," The Review of
Economics and Statistics, XXXIV (May, 1952), 143-155.

4. W. Z. Hirsch, "Progress Functions of Machine Tool Manufacturing,"
Econometrica, XX (January, 1952), 139.

5. A. D. Searle, "Productivity Changes in Selected Wartime Ship-
building Programs," Monthly Labor Review, LXI (December, 1945), 1132-1147.

6. K. A. Middleton, "Wartime Productivity Changes in the Airframe
Industry," Monthly Labor Review, LXI (August, 1945), 215-225.

7. W. B. Hirschmann, "Profit from the Learning Curve," Harvard Busi-
ness Review, XLII (January-February, 1964), 125-139.

8. National Aeronautics and Space Administration, Guidelines for
Evaluation of Contractor Accounting Systems, NHB 9090.6 (February, 1967
Edition), Para. 905.

9. National Aeronautics and Space Administration, Procedures for
Reporting Cost Information from Contractors, NHB 9501.2 (March, 1967 Edi-
tion), pp. 57-58.

10. For example, Alpha and Omega and the Experience Curve, Directorate
of Procurement and Production, U. S. Army Missile Command, Redstone Arsenal
Alabama (April 12, 1965). Also, "Improvement Curve Analysis Techniques,"
Defense Contract Audit Manual, Appendix F (July, 1965).

11. A. W. Levi, Varieties of Experience (New York: The Ronald Press
Company, 1957), p. 3.

12. Some philosophical views on experience have been discussed in
Levi's work. For a unique approach, H. T. Deinzer's Development of Account-
ing Thought (New York: Holt, Rinehart and Winston, Inc., 1965), Chapter IV,
can serve as an excellent reference.

13. J. A. McGeoch and A. L. Irion, The Psychology of Human Learning
(New York: David McKay Company, Inc., 1961), p. 2.











14. E. R. Hilgard and G. H. Bower, Theories of Learning (3rd ed.
New York: Appleton-Century-Crofts, 1966), pp. 1-2.

15. Ibid.

16. R. Bellows, "The Management of Learning: Theory and Practice,"
Personnel Administration, XXIII (January-February, 1960), 22-28.

17. H. Asher, Cost-Quantity Relationships in the Airframe Industry,
Project RAND R-291 (California: The RAND Corporation, July 1, 1956), p.
191.

18. T. P. Wright, "Factors Affecting the Cost of Airplanes," Journal
of Aeronautical Sciences, III (February, 1936), 122-128.

19. A. B.Berghell, Production Engineering in the Aircraft Industry
(New York: McGraw-Hill Book Company, Inc., 1944), Chapter XII.

20. K. F. Hammer, "An Analytical Study of 'Learning Curves' as a
Means of Relating Labor Requirements to Production Quantities" (unpublished
master's thesis, Cornell University, 1954).

21. Asher, op. cit., p. 9.

22. Hirsch, Review of Economics and Statistics, p. 143.

23. The one reference mentioned was Paul A. Samuelson, Economics:
An Introductory Analysis (New York: McGraw-Hill Book Company, Inc., 1948),
pp. 473-474.

24. A. A. Alchian, "Costs and Output," The Allocation of Economic
Resources, M. Abramovitz et al. (California: Stanford University Press,
1959), pp. 23-40.

25. J. Hirshleifer, "The Firm's Cost Function: A Successful Recon-
struction," The Journal of Business, XXXV (July, 1962), 235-255.

26. "The Field of Management Accounting," N. A. A. Bulletin, XLIV,
Section III (June, 1963), 7.

27. Several textbooks can be referred to for a detailed treatment
of the nature and scope of managerial accounting. To suggest one: C. L.
Moore and R. K. Jaedicke, Managerial Accounting (2nd ed., Dallas: South-
Western Publishing Co., 1967).

28. For further details, refer to Chapter II.











CHAPTER II

EXPRESSING THE DYNAMIC RELATIONSHIP BETWEEN COST OR PRODUCTION TIME
AND THE QUANTITY PRODUCED


Purpose and Organization of the Chapter

Before an investigation can be undertaken to study the derivation

and understand the implications of the experience factor for managerial

accounting, it is necessary to review and consider what has already been

done in this direction. That a relationship exists between production

time or cost and cumulative production is by no means a contribution of

this study, for a considerable amount of work has been done to support

this contention. Unfortunately, literature available on the subject,

though abundant, often appears to be over-simplified, vague, and even

contradictory, mainly due to the fact that most authors prefer to follow

the accepted "pattern," and rely on "theories" based on implied assump-

tions without a proper understanding of their implications. Most of the

information on the production time-quantity relationship is available

under the subject-title "learning curve," or "progress curve," and al-

though the subject of this research is closely connected to the "learning

curve," there is a significant difference which will be noted in the

course of this study.

The main intention of this chapter is to investigate the "learning

curve" theory as an explanation of the dynamic production time-quantity

or cost-quantity relationships as observed in industrial situations.

Does the "theory," as proposed and accepted by so many authors and prac-

titioners, really serve as a reliable representation for ordering exis-











tential and conceptual data to aid business management in its function

of decision-making? An answer to this question has been the principal

aim of the chapter.

In order to obtain an acceptable answer, it has been deemed neces-

sary to trace a short historical sketch of the "learning curve" concept,

observe its acceptance and applicability, and define its characteristics.

The different "theories" and their implied assumptions as "accepted" over

the years have been explained and critically evaluated in the course of

the chapter, keeping the managerial accountant's point of view in mind.

Particular emphasis has been placed on analyzing the "linearity assump-

tion" as a means of expressing production time-quantity relationships,

since most of the accounting literature seems to imply a universal appli-

cability for this form of representation.

This investigation is supposed to pave the way for Chapter III,

where more detailed analysis of possible production time-quantity rela-

tionships which could be profitably utilized by the managerial accountant

have been indicated.


A Historical Sketch of Contributions to the Establishment
of a Cost-Quantity Relationship

Pre-World War II experience

It was in the airframe industry that peculiarities and trends in

production time-quantity relationships were initially observed. Miguel

A. Reguero has asserted that the credit for original investigation of air-

frame production data should be bestowed upon Leslie McDill, Commanding

Officer at McCook Field (predecessor of Wright-Patterson Air Force Base,











both near Dayton, Ohio).1 Reguero's research indicated that it was

McDill's efforts in 1925 which led to the formulation of the "learning

curve theory."2

However, Dr. T. P. Wright has generally been looked upon as the

pioneer who researched into the implications of continuous production.

T. P. Wright, while still a manager of the Buffalo plant of Curtiss-

Wright, presented a paper for the Aircraft Operations Session at the

Fourth Annual Meeting of the Institute of Aeronautical Sciences, which

was later printed in the Journal of Aeronautical Sciences, February, 1936,

under the title "Factors Affecting the Cost of Airplanes." In this paper

Wright pointed out that he became interested in the effects of quantity

production on cost around 1922, and the results of his empirical inves-

tigations have been graphically presented in the above-mentioned article.

This publication was the first attempt at a graphical representation of

production data on logarithmic graph paper, and the first attempt at de-

fining the linear dynamic cost function. Wright observed that as cumu-

lative production increased, the average cost per unit of the product in

question decreased. Not only did it decrease, but this decline followed

a particular pattern. It was noted that the average labor and material

cost per unit declined by a constant percentage with every doubled quan-

tity produced. Thus, when plotted on logarithmic graph paper the curve

that resulted was a negatively sloped linear function.

This, then, was the first mention of what was later referred to as

the "learning curve." An interesting point in Wright's article is his

classification of cost into the three elements of labor, material, and











overhead, for purposes of analysis. Most students of the subject would

partially concur with S. A. Billion, who observed that "although it is

now a widely acknowledged fact that labor and overhead vary as the quan-

tity of units produced is increased, there has been a surprising lack of
5
development on the direct material curve which Wright has suggested."

There does not appear to be any other important work on the impli-

cations of quantity on cost or production time between 1936 and the be-

ginning of World War II, and perhaps the next publication may be the non-

dated study by J. R. Crawford for Lockheed Aircraft Corporation.6


During and after World War II

Since 1940, several individuals connected with varied disciplines,

corporate bodies, and research institutions have contributed to the study

of production time-quantity or cost-quantity relationships. Although the

temptation to undertake a detailed evaluation and review of the historical

significance of the different contributions is very strong, such an

endeavor has been by-passed, for other capable treatments of the subject

are available. For example, Harold Asher's Cost-Quantity Relationships

in the Airframe Industry provides an excellent treatment of the histori-

cal reconstruction and evaluation of literature on the subject, from

Wright's first article to 1955, around which time Asher's work was
7
published.

In order to avoid duplication, a mere mention is made of the im-

portant contributors and their contributions. Only publications which

have not previously been commented on, and which have been considered

significant for this study, have been reported.










The work of J. R. Crawford of Lockheed Aircraft Corporation needs

special mention.8 Crawford was one of the most respected authorities on

the subject, and as such was called upon to conduct special studies by

the Stanford Research Institute and the Air Material Command of the

United States Air Force. Working along with Edwin Strauss, the now-famous

Crawford-Strauss Study was published for the Air Material Command in

1947.9

The contributions of P. B. Crouse,10 A. B. Berghell,11 K. A.

Middleton,12 G. W. Carr,13 G. M. Giannini,14 P. Guibert,15 E. Mensforth,16

W. Z. Hirsch,17 F. S. Hoffman,1 and Armen Alchian19 have been commented

on at length by Harold Asher.20 The only notable work missing in this

list of earlier contributions is that of A.D. Searle, who made a study

of the U. S. shipbuilding industry for the Monthly Labor Review in a

manner similar to that of K. A. Middleton, whose study had been conducted

on the airframe industry.21 The works of Miguel Reguero22 and Harold

Asher23 have been commented on, and evaluated, by R. P. Zieke24 in his

unpublished thesis, submitted to Stanford University.

The Harvard Business Review published an article by Frank J.

Andress which, in the opinion of this writer, is an excellent introduc-

tory article on the subject, in which the "theory" of the learning curve

has been explained, limitations pointed out, steps for application

enumerated, and mention made of different industries that could profit-

ably use the learning curve.25 A decade later, another noteworthy

article was published in the Harvard Business Review, by Winfred B.

Hirschmann, in which the long-run effects of experience were pointed out











and substantiated by empirical evidence.26 Hirschmann's thesis appears

to be that improvement can continue indefinitely, and can be actually

produced, or enhanced, by a concerted effort on the part of higher manage-

ment.

The field of industrial engineering has produced considerable work

toward the study of production-time-quantity relationships. A notable

contribution from this area has been the work of R. W. Conway and A.

Schultz.27 Along with the various observations made in their exhaustive

article are published the results of a study conducted using four firms

which had not used dynamic production data for control purposes. It was

found that although cost declines were evident, there appeared to be a

leveling off in a few cases where production had reached large quantities.

The results of an empirical study involving three hundred Southern

California metal product manufacturers have been presented by Reno R.

Cole.28 According to this study, 61 per cent of the respondents stated

that they used learning curves, although most suggested caution in its

usage.

An article by E.B. Cochran, which has hardly ever received mention,

is nevertheless worthy of comment.29 Cochran has asserted that the learn-

ing curve technique has been dying in popularity due to certain inherent

weaknesses. He made a careful examination of the basic cost function,

and attempted to develop new concepts, including the suggestion for a

"unit of learning." It has been implied that the linearity assumption

(as will be discussed later in this chapter) can be misleading, and the

proper functional representation may be the S-shaped curve, referred to

earlier by G. W. Carr.30











A much heralded, but a rather disappointing study was undertaken

under the aegis of the Institute of Business and Economic Research at the

University of California by E. C. Keachie.31 With the help of a question-

naire and a guided empirical study, Keachic attempted to substantiate the

thesis that production time-quantity relationships are as important to

small business management as to the larger firms, irrespective of the

industry with which they are connected.

Reference to the implications of dynamic production data has also

been made in accounting literature by a few writers. Mention must be

made of Rolfe Wyer,32 Ronald Brenneck,33 R. B. Jordan,34 Sanders and Bly-

stone,35 V. J. Shroad,6 and Arnett E. Burrow,37 among the various ac-

countants who have referred to the factor of experience as an important

element which should be taken into consideration for accounting analyses.

Contributions made by corporate bodies and research institutions

cannot be bypassed in a historical reconstruction of this nature. Almost

all of the major aircraft corporations have issued manuals and studies--

one of these mentioned earlier regarding J. R. Crawford's work for Lock-

heed Aircraft Corporation.38 Special mention may be made of Tommie

Fowlke's manual for Convair Corporation, which was recently re-issued by

General Dynamics, Fort Worth.39 The distinct approach and the care for

detail illustrated by Fowlkes was of considerable interest to the present

study.

A considerable amount of research has been accomplished at two
40
research institutions: The Rand Corporation, and the Stanford Research
Institute.41 Most of the studies were financed by the Air Material C
Institute. Most of the studies were financed by the Air Material Com-











mand of the United States Air Force, and no student of the subject at

hand could conduct a study without indicating his appreciation to the

Armed Services of the United States of America for their role in the

development of knowledge in this field.


Development of the Linear Logarithmic Dynamic Cost Function

T. P. Wright's "Eighty Per Cent Curve"

The implications of quantity produced on the production time and

cost of the product were first noticed in airframe production, as pointed

out earlier, and the relationship was initially referred to as the "eighty

per cent curve."42 To quote T. P. Wright, "This 'eighty per cent' has a

definite meaning in that it represents the factor by which the average

labor cost in any quantity shall be multiplied in order to determine the

average labor cost for a quantity of twice that number of airplanes."43

In other words, the average labor cost per unit of product indicated a

20 per cent decrease between doubled quantities. Thus, if the cumulative

average labor cost for the production of ten units happened to be $10,000

and if ten more units were produced, the cumulative average for all the

twenty units would be $8,000 per unit; that is, a 20 per cent decline in

average labor cost with an equivalent production in units.

This "eighty per cent curve" came to be generally accepted, espe-

cially by the Pacific coast airframe manufacturers, although used by some
44
under a different interpretation. For example, J. R. Crawford of Lockheed

Aircraft Corporation agreed with the linear relationship, but he felt that

such a relationship existed between the quantity produced and the individual
unit man-hours, as opposed to the cumulative average.45 Another variation
unit man-hours, as opposed to the cumulative average. Another variation











was where lot-averages were plotted against unit costs or labor hours to

arrive at linear functions for the "eighty per cent curve."46

It was not long before the hazards of generalization were noticed

and separate functions were derived by each company to suit its peculiar

production process and product. The generality of the "eighty per cent

curve" has been indirectly refuted over the years in various ways by

students of the dynamic relationship. An early study which directly

challenged the validity of an industry-wide "eighty per cent curve" was

undertaken by A. Alchian who asserted that the available statistical evi-

dence was overwhelming against its general application. He concluded

that:

Extensive analysis by the Economics Division of the RAND
Corporation indicates beyond all doubt that the slopes are
different and that the heights are different among the
plants producing airframes. Even between two manufacturing
facilities producing the same type of airframe the heights
and slopes are different.47

This assertion was restated by Alchian in another Rand study pub-

lished a few months later.48 In this later study, Alchian used statisti-

cal analyses involving predicted and actual values to determine the reli-

ability of different types of average curves. The data seemed to indicate

that absolute differences between predicted and actual values (properly

weighted by actual man-hours) averaged 25 per cent of the actual, where

predictions were based on an industry-wide average curve, and also where
49
predictions were based on a general airframe-type progress curve.4

This analysis cast considerable doubt on the acceptance of "general-

average" type projections, and indicated the necessity for further re-

search into each specific situation.











During and after World War II

Since the beginning of World War II, interest in the production

time-quantity relationship has spread to areas other than the airframe

industry, and reference has usually been to the "learning curve" or the

"manufacturing progress curve" concept and technique. This learning curve

refers to the resultant function of production data plotted on logarithmic

graph paper, indicating a constant percentage decline in costs or labor

hours between doubled quantities. This is the same as the "eighty per

cent curve" referred to earlier, except that the learning curve slope

could represent any mathematical quantity between a feasible range and

not just one point within this range.

Although this concept of cost-decrease due to improvement or ex-

perience or learning has come to be known by many other names, it is still

most popularly referred to as the "learning curve." Appendix A contains

a list of various names used to describe the relationship between cost or

labor hours and quantity of production.

The last two decades have witnessed a slow but steady acceptance

of the concept and technique by industries outside the airframe production

type. A few industries where production time-quantity relationships have

actually been utilized for decision making (as differentiated from where

the relationship could be utilized) have been mentioned below.

Reno R. Cole's study, referred to earlier, indicated that 61 per

cent of the 300 Southern California metal product manufacturing industries,

other than airframe, utilized the cost-quantity relationship.50 Included

in this list of industries were precision mechanical electro-optical











instruments, electronic unit manufactures, mechanical-hydraulic electri-

cal unit manufacture, large built-up laminated plastic aircraft assemblies,

and electronic data processing equipment manufacture.

Application of labor cost-quantity analysis to a multi-product

industry has been claimed by Paul F. Williams on the basis of data col-

lected at United Control Corporation.51

In an unpublished paper presented on behalf of International Busi-

ness Machines Corporation, Donald A. Schreiner has given examples of how

productive time-quantity relationships have been utilized to aid opera-

tions at I. B. M., Endicott.52 The point that management is considerably

aided has been strongly asserted.

E. C. Keachie's recent study, mentioned earlier, has pointed out

the benefits derived by small manufacturers who utilized the relationship.53

The usage of dynamic production data by small manufacturing firms was

evidenced by this author while on a visit to a small walkie-talkie manu-

facturing plant employing around thirty people. It was surprising to find

the accountant maintaining elaborate charts depicting production time-

quantity relationships, which he asserted were very helpful to him.

W. B. Hirschmamin his study has shown its application to several

industries such as petroleum, electric power, basic steel, and construc-

tion. Included in his group of examples are actual situations encountered

including one involving DuPont's petrochemical works.54

John N. Sidrsema has indicated the application of the learning

curve by a high frequency electronic tube manufacturing concern. An in-

teresting point in his presentation is a description of the company which











was studied, including details regarding the accounting systems and pro-

cedures followed.55

In the course of private correspondence with the author of this

study, Irving J. Sandler, Chief, Special Projects Division, Defense Con-

tract Audit Agency, has presented an interesting list of industries and

functions in connection with which the Agency has applied the experience

curve methodology. Included in this list are the manufacture of electri-

cal and electronic components for major weapon systems, manufacture of

controls and instruments for a variety of propulsion systems, munition

applications, and missile production activities. Sander is emphatic in

his assertion that the "analytical technique is by no means confined to

the airframe production industry."56


The Learning Curve

The learning curve is a statistical or mathematical representation

of production data which can be used to aid management in the functions

of planning and control. It is based on the concept that as operation is

repeated, there is opportunity for experience to generate improvement,

which leads to lower production time or cost for subsequent units manu-

factured. Thus, as a task is duplicated, the learning derived through

repetition gets embodied into lower costs or production time for later

quantities produced.

An hypothesis has been stated in the form of the learning curve

"theory," to be used in business or manufacturing situations, based on

this phenomenon of improvement. The phenomenon should be differentiated

from the learning curve "theory," as the "theory" is supposed to provide











a means for ordering data to aid management in the task of planning and

control in actual industrial situations.

The concept of "learning" has also been used to develop another

type of projection referred to as the "learner curve" or sometimes as

the "learning curve," which has been utilized for incentive wage payment

schemes. The discipline of psychology has also been concerned with the

phenomenon of learning and graphical projections, often referred to as

"learning curves," which have been used for clinical analyses. To avoid

any misconceptions regarding these "learning curves," a detailed distinc-

tion has been attempted below.


A distinction between three "learning curves"

It may be unfortunate that the dynamic production time-quantity

relationship has come to be referred to as the "learning curve." There

are two important reasons for the above contention.

In the first place, the word "learning" implies a narrower appli-

cability of the dynamic production time-quantity relationship than what

this relationship actually involves. The term "learning" often gives the

impression that the concept is applicable only to the worker who is directly

connected with production operations. In other words, a false impression

regarding the applicability of learning on the part of the direct laborer

as the only criterion which leads to improvement with increased produc-

tion may be generated. The truth is that the "learning curve" concept

as used by management is concerned with improvement gained in several

different ways, of which the individual worker's learning can be con-

sidered only a contributing factor, as indicated in Chapter IV.











A more important reason for considering the term "learning curve"

as inappropriate lies in the fact that the same term has been used to

refer to other more appropriate tools, concepts, and techniques. For

example, psychologists have used "learning curves" to measure and analyze

learning trends in individuals, and it is perhaps this usage which led

to the term being borrowed for production data analyses. The term "learn-

ing curve" has also been used for a graphical representation to aid in-

centive payment schemes where experience at the job might be an important

criterion for efficient production.

Although all three "learning curves" deal with the phenomenon of

learning, or experience, or improvement, each is used to serve distinct

functions. The psychologist's learning curve deals mainly with learning

patterns as observed in individuals, and has been used in psychological

analyses to answer questions such as, how or why does learning take

place in a particular individual under peculiar conditions? Also, what

can be done to improve learning? In other words, the curve helps in

analyzing learning as a mental process.

An excellent reference on the use of learning curves in psychologi-

cal analyses has been provided by McGeoch and Irion's The Psychology of

Human Learning.57 The authors define a "learning curve" as a line of

regression of performance upon practice, where practice is the known vari-

able and performance, as a result of practice, is the unknown.58 Figure

II-1 indicates representative forms of learning curves when trials or some

other measure of practice are plotted on the X axis and the corresponding

measures of performance on the Y axis. An example of an actual learning


















A





C
B














Practice









FIGURE 11-1
REPRESENTATIVE "LEARNING CURVES" AS USED FOR
PSYCHOLOGICAL ANALYSES










curve of one practiced subject for learning a list of words has been

illustrated in Figure 11-2. McGeoch and Irion state, "there is no single

curve of learning which can be called the curve of learning. Different

tasks, experimental procedures, methods of measurement, and types of subject

will yield different forms of learning curves."59 The point to be noted is

that these learning curves are derived by observing individuals at particular

tasks under experimental conditions.

The graphical representation used for purposes of providing wage

incentives has often been referred to, more appropriately, as the "learner

curve." An example of a learner curve has been illustrated by L. A. Barron,

who has used a descending step-like formation to indicate a means for compen-

sating new workers during the learning period.60

Frank J. Powers has provided a graphical representation which he

has referred to as the "learning curve" to help develop realistic incentives

for workers on short-run jobs.61 Figure II-3 is an example of such a learn-

ing curve on arithmetic grid paper.

The use of logarithmic graph paper to determine incentive learning

curves was initially explained by J. R. Hadley, who illustrated his learning

curve as an upward sloping linear function.62 Logarithmic paper has also been

used by Lou Wertman, whose learning curves for individual workers are very

much like the projections used for business decision-making.63

It has been noted that although these "learning curves" incorporate

the same phenomenon used to describe production cost-quantity relationships,

there is a difference of purpose and a variation in means employed in the

process of calculation. Although these two learning curves may be considered









































2 3 4 5 6 7 8 9 10 11 12
Trials


FIGURE II-2
AN ACTUAL LEARNING CURVE DERIVED IN
A PSYCHOLOGICAL EXPERIMENT



a- me sa manach, and L. hton Tu Pvason num Leram ne vers~ avw -..~~ us. cmpnyhe me be Ipo 2a














-Y









0 110


100

0
-o

a. 90


80

u 70

S o

60

Learning Period


Time in Days










FIGURE 11-3
AN EXAMPLE OF A "LEARNING CURVE"
USED FOR AN INCENTIVE WAGE PAYMENT SCHEME












as elements of the same species, there are significant differences, there-

fore distinct references may be advisable.

In the opinion of this author, the term "learning curve" is best

suited for the psychologist's graphical representation, and is certainly

less descriptive of the phenomenon considered under the production time-

quantity relationship used for business decision-making. The graphical

representation used for wage incentive schemes may be appropriately re-

ferred to as the learner curve to signify its applicability to incentive

schemes.

The terms "experience curve," "progress function," "improvement

curve," or "time-reduction function" appear to be more descriptive of the

phenomenon involved in the production time-quantity relationship as uti-

lized for business planning and control, than the more accepted title

"learning curve."64 For the remainder of this report, the "learning curve"

used for business decision-making will be referred to as the "experience

curve," to differentiate it from the other two namesakes.


Alternative means of projecting data

The importance of the experience curve has been based on the under-

standing of a basic mathematical concept--the logarithmic scale. Almost all

explanations available on the subject utilize the logarithmic scale in

preference to the arithmetic scale, and the value of the experience curve

as a tool for planning and control has been made dependent on the successful

use of logarithmic scales. The reasons for this approach are explained

below.

A graphical representation of continuous production data can be











obtained by plotting costs or labor hours per unit against the number of

units produced. Consider the hypothetical production data presented in

Table II-1. A mere glance at the table indicates that the labor hours

per unit have been declining with increased production. This information

when plotted on arithmetic grid graph paper appears in the form of a

hyperbolic function, indicating a fast initial decline which straightens

out and turns asympototic to the X axis, as seen in Figure 11-4. The

reason for this functional form is that plain arithmetic grid graph paper

represents equal amounts of differences by equal distances (denoted by the

spaces) in terms of absolute figures. Thus a change from one to two units

represents an absolute difference of one unit, just as the change from five

to six, or one-thousand to one-thousand-and one unit represents an incre-

ment of one unit. Although the absolute differences are the same in all

these cases, the relative differences are unequal. For example, the in-

crease from one to two units represents a 100 per cent increase, from five

to six is a 20 per cent increase, whereas from a thousand to a thousand and

one units represents an increase of only .01 per cent.

It is usually argued that if one's intention is to visualize a re-

lationship between two variables in the initial stages of production, then

the non-linear graph might prove advantageous. In other words, for a "quick"

look at the effect of experience on initial units produced, this function

might serve the purpose. However, if it were necessary to obtain data

through extrapolation (or even interpolation), especially for extremely

large quantities, this curve might prove inefficient and cumbersome. For

example, to plot data for five thousand units, the graph would have to be











TABLE II-I

Selected Values from an Hypothetical Cumulative Production Schedule




Unit Number Labor Hours Unit Number Labor Hours


1 100.000 40 30.488
2 80.996 50 28.375
3 70.205 75 24.902
4 63.994 100 22.699
5 59.557 250 16.899
6 56.161 500 13.519
7 53.441 1,000 10.814
8 51.192 2,500 8.051
9 49.287 3,750 7.066
10 47.643 4,960 6.457
15 41.812 4,970 6.453
20 38.113 4,980 6.448
25 35.470 4,990 6.445
30 33.448 5,000 6.441
35 31.828 5,500 6.246










0


O'



zr


eO
Z M






OC
o
0





S C-
0- C4


oG












z
0 .0
J l o







C4
---
CL
N
10






4'-











00



Labor Hour 4 0
-I
0 .= .











extended 125 times horizontally, and the projection for the last forty

units would then be as in Figure I-5. The absurd length of the graph,

plus the limited value of the projection at high production levels re-

stricted utility for this mode of presentation. However, this argument has

not been found acceptable by this study for reasons explained in Chapter IV.

Some of these shortcomings of the arithmetic grid graph paper can

be avoided, it is asserted, by plotting the data on logarithmic grid graph

paper. Thus, if the data presented in Table I were plotted on logarithmic

graph paper, the result obtained would be a negatively sloped linear func-

tion as shown in Figure 11-6, which would be expressed mathematically as

the linear exponential function: Y = A X-B (indicating a constant rate of

decline).

In other words, if the intention is to measure relative rates of

change, rather than absolute amounts, without being influenced by the size

of numbers, then the data have to be plotted on logarithmic graph paper

which can indicate relative relationships.66 Just as the distance between

units two and four would be the same as the distance between units ten and

twelve on arithmetic grid paper, that is, the absolute differences being

represented by two units in both cases; logarithmic graph paper is so con-

structed that equal distances represent equal percentage changes. Thus,

the distance between two and four units, which represents 100 per cent

change, would be equal to the distance between units three and six, or

units five and ten, or units seventy and 140, etc., each of which repre-

sents 100 per cent change. The logarithmic graph paper referred to is the

full logarithmic paper, or one with both axis marked in logarithmic scales,









0
0
0




Z
I-


I-





0 0 o

>





0Z


ca
d Iz a

u > u 1



r Uv
Ew o

Z o







0
a o4u






Labor Hours Per Unit











40







0 w N '0 a
S "
' n: LU o>0
o.bo Hour Pe U











as already seen in Figure 11-6 which is different from semi-logarithmic

paper which has one logarithmic scale and another arithmetic scale.67 Full

logarithmic graph paper is constructed so that distances between numbers

on either scale represent equal percentage changes. This full lo.ga'rithmic

graph paper is also referred to as double-log, full-log, log-log, rate,

slide-rule, and ratio-graph paper.

The following list is an adaptation of observations made by

Kroeker and Peterson who have pointed out several characteristics of loga-

rithmic graph paper.9

a. A straight line on logarithmic paper means that the rate of

change between two variables is a constant.

b. There are no zeros--values approach zero, but never achieve it.

c. The graph paper is drawn in terms of cycles such that the first

cycle starts with one and ends with ten, the second cycle denotes values from

ten to 100, the third from 100 to 1000, and so forth.

d. Entire cycles may be omitted, but one cannot start a cycle

from the middle of a range. Thus, the first line has to start with a one,

or a ten, or any integral of ten, or the reciprocals of those numbers for

values less than one, but not with any other figure.

e. Once an absolute value has been assigned to a point on either

axis, all other locations on that same axis have a fixed absolute value such

that comparable locations in each successive cycle have an absolute value

exactly ten times as great as the value in the preceding cycle.

With the help of this logarithmic graph paper the rate of change

over the entire range of production can be better visualized, and the trend
























































Labor Hours Per Unit











line for planning and control purposes more efficiently utilized. It may

be reiterated that the trend line need not be linear, for as long as a

pictorial quantification of production data can be indicated, such a repre-

sentation can be utilized as explained later.

It would be pertinent to point out that although the advantages of

logarithmic scale utilization have been well appreciated by this study, the

overemphasis on this mode of analysis has also been noted. Further discus-

sion of the subject has been undertaken in Chapter IV, where the findings

of this study, as contrasted to accepted procedures just pointed out, have

been discussed in detail.


Characteristics of the experience curve

I. Since the cost per unit varies inversely with the quantity

produced, the function would be negatively sloped. An upward sloping curve

is possible, but would signify deterioration or inefficiencies through gain-

ing experience, which would be unusual but possible.

II. The function is a dynamic cost function, and not a static

cost function, as it is the cumulative production which is one of the vari-

ables, and not "rate" of production. This point was discussed earlier in

Chapter I.

III. Technology is not assumed to be constant. As a matter of

fact, it is the changing technology which is depicted by the lower costs.

A distinction is made here between technology changes and changes

in the techniques of production as pointed out by A.Alchian.70 Technology

is taken here to refer to the state of knowledge, whereas techniques of

production refer to fixed assets such as land, equipment, and production











processes. In other words, a change in technology refers to improvement

on the part of the workers, supervision, management, better engineering

design, more efficient tooling, smoother coordination between functions,

along with other factors mentioned in Chapter IV. Techniques of produc-

tion are taken here to refer to what is commonly considered in accounting

terminology as "capacity to produce." If the relationship analyzed is for

a product, changes in the techniques of production might necessitate a new

curve, and hence they are assumed to be constant. On the other hand,

changes in the techniques of production, when quantified, might indicate the

efficiency derived through experience, if curves are plotted for entities or

industries, in which case even the techniques of production may be considered

variable. However, where individual products are concerned, production

capacity is assumed to be constant, whereas technology is considered vari-

able.

IV. Yet another characteristic is that the data signify continuous

production. In other words, if production on this product or process is dis-

continued for a substantial period of time, such that the experience gained

may be adversely affected, then the shape of the learning curve would also

be affected. Therefore, in order to arrive at a linear function, continuous

production has to be assumed.

V. There is an assumption of homogeneity of product or process for

which the learning curve has been plotted. Minor design changes would be

incorporated into the same curve. However, substantial changes would neces-

sitate a new function.

VI. There has to be consistency in the type and mode of data col-

lection, such that differences in data do not affect analysis.











VII. The percentage attached to the learning curve indicates the

rate of improvement. This rate implies a constant percentage of decrease

with doubled quantities, and is expressed by the complement of this rate

of decrease. Thus, as discussed earlier, the 80 per cent slope indicates

that the decrease in costs between doubled quantities would be 20 per cent

at all levels of production. In other words, once the learning curve slope

has been established, the percentage decrease would be the same for, say,

increase in production from one to two units, or twenty to forty units, or

300 to 600 units, or even from 1,000,000 to 2,000,000 units. This is

mathematically expressed by the linear function Y = AXB It is this

characteristic that initially created an interest in the experience curve.

The simplicity of the straight line with which one could utilize production

data for more accurate forecasting, which was implied by the linear charac-

teristic, was responsible to a considerable degree for the early acceptance

of the experience curve; and by the same token, it is this simplicity which

might be responsible for its stunted growth.

VIII. The reference to a "linear" logarithmic function does not

imply that production data have to fall exactly on the smooth path. When

plotting actual data the chances of finding a smooth straight line are al-

most phenomenal. However, a smooth projection may be derived by using

statistical tools, such as the line of best fit using least-square compu-

tations. In other words, a relative decline may be evidenced by observing

the plot points through which the line of best fit can be drawn. Such a

line may be drawn for the cumulative average or individual units hours or

average unit hours, depending on the observer's judgment regarding











linearity.7 More on this subject of statistical implication will be

discussed in Chapter IV.


A Critique of the Conceptual Implications of
Experience Curve "Theories"

What is the "theory" behind the experience curve? As initially

stated by Wright, the answer might be phrased as something to this effect:

as production is doubled, the average labor cost per unit declines by a

constant percentage, between the doubled quantities.72 That is, if

cumulative average cost per unit were to be plotted against the cumula-

tive number of units produced, the result would be a linear function on

logarithmic graph paper.

However, the airframe manufacturers and users of the experience

concept in a few other industries found that the above statement could be

refuted on grounds of empirical data collected which indicated that the

cumulative average when plotted on logarithmic graph paper was not a straight

line, at least not in the initial stages of production. Several users con-

tended that it was the unit hours as plotted against cumulative production

that resulted in a linear function, and the cumulative average function was

curvi-linear in the initial stages of production.73

Yet another interpretation, one which was (and still is) widely

accepted, requires plotting averages for specific lots against cumulative

production and arriving at a linear cost function which is referred to as

the lot average learning curve.74

Beyond the initial production, it is usually agreed by proponents

of the experience curve theory that the curve will follow a linear trend.










In other words, once the curve has settled down, one would find a fairly

straight projection from further production provided there are no substan-

tial changes.

What the theory involves is interesting to note. It implies that

once a few values for units produced are secured, this limited information

can be used by management in decisions regarding planning and control of

operations, for the theory states that a definite pattern of constant per-

centage cost decreases for doubled quantities will ensue. The universality

of acceptance awarded this proposition is overwhelming despite several

studies made which seem to point out the possibilities of other forms of

the production time-quantity functions. It is acknowledged that several

studies have been conducted which seem to indicate a high degree of correla-

tion for the linear representation; however, the point to be noted is that

there are as many empirical observations which have indicated non-linear

trends.

In other words, there is empirical evidence to support any of the

contentions above, that either the cumulative average curve or the unit hours

curve or the lot average curve can be plotted to arrive at a linear function

on logarithmic graph paper. However, there are other findings which in-

directly challenge the contention of linearity. For example, Gardner Carr

formulated what he called an S-shaped curve.75 Wright had pointed out the

possibility of a gradual levelling-off curve.76 This pattern was also ob-

served by Conway and Schultz, among others.7 The Stanford Research Insti-

tute insisted on the recognition of a humped curve to represent initial

production.78 Discussion on these and other different patterns has been











avoided at this point, for a major portion of the next chapter has been

devoted to the different patterns observed in production time-quantity or

cost-quantity relationships. The.point is that if the linear representa-

tion can be proved to be conceptually sound as well as empirically verifi-

able, then a universal proposition can be stated in the form of a "theory."

However, if contrary assertions can be made, the proposition cannot be

stated in the form of a "theory," but may be presented as a possible ex-

planation for a particular set of conditions, or can be used as an approxi-

mation for purposes of analyses simplification. The remainder of this

chapter represents an investigation of the conceptual inconsistencies

involved in the acceptance of a linear projection, whereas the next chapter

contains an investigation into some emprical findings.

It is acknowledged in the field of cost accounting that the total

cost of a product is composed of several elements which can be recognized

as having been incurred for the production of the product. As regards

manufacturing or production cost, segmentation of portions applicable to

direct material, direct labor, and manufacturing overhead is undertaken

to facilitate managements planning and control functions.79 Assuming that

the total cost of a hypothetical Product X can be classified into these

three segments, the effect of increased production can be analyzed by ex-

perimenting with the data presented in Table II-II.

It will be noticed that the material cost per unit is declining at

a much slower rate than the decline noticeable in the per-unit labor and

overhead costs. If the data presented in Table II-II were plotted on

logarithmic paper, the individual learning curves for material, labor,











TABLE II-II

Selected Cost Data for Product X


Complement of
Direct % Decrease be-
Unit Labor Material Applied Total tween Double
Number Cost Cost Overhead Cost Quantities


1 $200.00 $500.00 $100.00 $800.00
2 140.00 450.00 70.00 660.00 82.50
4 98.00 405.00 49.00 552.00 83.64
8 68.60 364,50 34.30 467.40 84.67
16 48.02 328.05 24.01 400.08 85.60
32 33.61 295.24 16.81 345.66 86.40
64 23.53 265.72 11.76 301.01 87.08
128 16.47 239.15 8.24 263.86 87.66
256 11.53 215.24 5.77 232.54 88.13
512 8.07 193.71 4.04 205.82 88.51
1024 5.65 174.34 2.83 182.82 88.83
2048 3.96 156,91 1.98 162.85 89.08
4096 2.77 141.22 1.39 145.38 89.27











overhead, and the total cost curve would be as shown in Figure 11-7. We

can observe that although the curves for the cost segments are declining

at a constant rate, the total cost curve which is a summation of the in-

dividual segments is not a linear function, but is convex to the point

of origin. The reason for this curvilinearity is obvious. The total

cost curve is a mere summation of the individual elements; hence, it will

first be pulled down by the cost element which has a steeper slope, but

after a certain point, its rate of decline will be lessened by the slower

decline-rate cost element, in this case, material cost.

The point that emerges is that if improvement takes place at the

same rate for all elements of cost, then the total cost line would be

linear on logarithmic paper. However, as will be seen, the opportunities

for improvements are more abundant where time taken for production is in-

volved than for cost of material content. The assumption that all ele-

ments contributing to total cost have the same rates of decline may not

be valid, and if this is so, the linearity assumption for the "learning

curve" would have doubtful validity. How valid is the linear represen-

tation for the different elements of cost? How much more reliable would

projections be if costs were broken down into different elements and

their relationships with quantity produced observed? Perhaps more accept-

able than the total cost-quantity relationship, but, then, these elements

of costs are individually made up of sub-elements. Thus the labor cost

would include costs incurred on different operations, which might be sus-

ceptible to different rates of improvement, as indicated below.

The labor hours expanded on a particular unit may be made up of

several different types of operations. For example, Asher has illustrated

















z


O





z

0-







z 0
>
0











oeO
IY








Q.



z
W z










0




0


Cost in Dollars











the effect of different improvement rates for major and final assembly,

sub-assembly, and fabrication, on the unit curve which turns out to be

considerably convex, as can be seen in Figure II-8, which has been adapted

from Asher's presentation.80

Yet another consideration may be the number of times an operation is

performed during the course of producing one unit. For example, while as-

sembling a special truck body, four gadgets of the same type might have to

be assembled and mounted. The opportunity for gaining experience in mount-

ing this gadget would be much more than another widget which has to be

mounted only once per truck. In other words, there could be different

rates of experience within the assembly operation on a unit, which could

lead to a curvilinear projection as in the other cases.8

To carry this line of reasoning a little further, it may be argued

that even within an operation there are sub-operations, sub-sub-operations,

etc. each having its peculiarities, leading to different rates at which ex-

perience can be gained. In other words, the main operation representing an

aggregate of these sub-operations might produce curvilinear trends depend-

ing upon the different rates of improvement for each of these sub-opera-

tions. A study undertaken at the University of Iowa, where a punch-press

operation was dissected into sub-operations (which were referred to as

therbligs), and learning patterns for different individuals for each ther-

blig studied, seemed to indicate different rates of improvement for the

different therbligs.82 If so, the projection for the entire operation is

likely to be curvilinear, although the chances of offsetting rates might

produce a quasi-linear trend. Of course, the curvilinearity for each







































































4!un Jld sjnoH JoqDl










operation might be insignificant by itself; however, when several opera-

tions are aggregated the total labor curve might be significantly affected.

Another inconsistency which can be pointed out pertains to the

dependent variable. It is not uncommon to find direct labor hours plotted

against cumulative production to arrive at the linear projection. Neither

is it uncommon to find total costs being used in place of direct labor

hours. Sometimes even man-hour cost per unit, or direct man-hours-per-

pound (as often used in the airframe industry) are represented on the or-

dinate. In other words,several different variables have been used, depend-

ing upon their suitability at depicting a straight line projection. But,

then, total direct labor hours are not the same as direct labor cost or

total unit cost. They do not necessarily have an absolute relationship

with direct labor cost, and certainly not with total cost. For example,

if an incentive wage payment system has been employed, it might very well

be that the decrease in labor hours would be offset to a considerable de-

gree by the increase in the labor rate to indicate no marked difference in

the labor cost. Or referring back to Table II-II, the rate of decline in

labor costs for increased output (a 70 per cent rate) is not the same as

the rate of decline for total cost, as indicated by column 4 of the same

table. Thus a decline in production time does not necessitate a proportion-

al decline in labor cost or total cost, since a perfect correlation between

direct labor hours, direct labor cost, or total cost cannot be generalized

a priori.

Hence, if a linear function results from using one of the above as

the dependent variable, a curvilinear function may be the result if the











other two are plotted. The point being brought out is that the experience

curve "theory" with its linearity assumption has a nebulous definition for

one of its determinants, a point which has hardly ever been discussed or

criticized in current accounting literature.

A question which often emerges in discussions concerning the learn-

ing "pattern" is: why is it that the constant percentage applies only to

doubled quantities and not to tripled or quadrupled quantities? Is there

something "inherent" in production processes that just leads to a certain

percentage decrease every time quantity is doubled? True, it is often ob-

served that when production data are plotted on logarithmic paper, one can

derive a straight line with the help of statistical tools such as determin-

ing the line of best fit with the help of the least-squares method, as

pointed out earlier. But is there any reason that production data might

not be such that there occurs a constant rate of decline for tripled quan-

tities? Assume the data hypothesized in Table II-III. This table has been

so constructed as to indicate an 80 per cent rate of decline for tripled

quantities. However, a straight line is projected when the information is

plotted on logarithmic graph paper as indicated in Figure II-9.

The reason for this seemingly peculiar result once more lies in the

construction of logarithmic scales where relative changes are indicated.

The distance between units one and three is the same as between three and

nine, or between nine and twenty seven, reflecting proportional changes.

Thus, what can be referred to as an 80 per cent experience rate for tripled

quantities is also an 86.8 per cent per cent rate of decrease for doubled

quantities. This indicates that what can be expressed by a rate of decline




74






TABLE II-III

Cost Data Signifying Constant Rate of Decline for Tripled Quantities



Unit Number Labor Hours Unit Number Labor Hours


1 100.0 15 57.6
2 86.8 20 54.4
3 80.0 27 51.1
4 75.4 35 48.5
5 72.1 42 46.8
6 69.4 50 45.1
7 67.3 60 43.5
8 65.5 70 42.1
9 63.9 75 41.6
10 62.6 81 40.9
11 61.4 90 40.0
12 60.3 100 39.2
































FIGURE II-9
CONSTANT RATE OF DECLINE FOR TRIPLED QUANTITIES
AS PROJECTED ON LOGARITHMIC-GRIDS


Cumulative Production











for tripled quantities. However, a straight line is projected when the in-

formation is plotted on logarithmic graph paper as indicated in Figure 11-9.

The reason for this seemingly peculiar result once more lies in the

construction of logarithmic scales, where relative changes are indicated.

The distance between units one and three is the same as between three and

nine, or between nine and twenty-seven, reflecting proportional changes.

Thus, what can be referred to as an 80 per cent experience rate for tripled

quantities is also an 86.8 per cent rate of decrease for doubled quantities.

This indicates that what can be expressed by a rate of decline for a tripled

or quadrupled quantity of production can as well be expressed in the conven-

tional manner as a rate for doubled quantity.

The above analysis does not invalidate the hypothesis that production

data can appear in forms other than the linear logarithmic type, neither

does it answer the question posed before: is there something "inherent" in

production processes which leads to the theorized linear form? It would be

foolhardy to answer this question in the affirmative. Production data might

take other forms, for example a constant rate of decline may be evidenced

for equal quantities produced, or with each unit produced.

It may be argued that it is "logical" to accept the contention that

human beings can indicate an equal amount of improvement with equal oppor-

tunity for improvement. However, a little thinking can upset the logic in

the argument. In the first place what is "equal opportunity for improve-

ment"? Even if this were true, that humans did improve an equal amount with

a doubling of the original work done (a psychological hypothesis which would

have to be empirically verified), why should this same contention apply to











the experience curve which is affected by the complex business organism

with its various components and functions. It is the contention of this

study that there can be no a priori assertions regarding a linear pattern.

The only thing that can be asserted is that the logarithmic scale, by bring-

ing relative changes into the limelight, tends to generate a quasi-linear

trend.

However, the point to be noted is that there is no scientific reason

for costs or production time to decline at a constant rate over an infinite

range of production. The fact is that statistical and mathematical tools of

approximation have to be utilized in order to generate a smooth linear trend

and on this very ground the "theory" can be strongly criticized, a charge

which has been undertaken in Chapter IV.

From the above critique it will be noticed that at the very most, the

experience curve "theory" is a rough approximation of production data as has

been observed in special situations. The attempt at creating a universal

proposition out of a simplified approximation might be one of the factors

which has led to the limited acceptance of the concept. The hypothesis

that experience promotes efficiencies which lead to a decline in cost with

increased production is still acceptable, but it might be dangerous to

generalize that such declines take place by means of a constant percentage

whenever quantities produced are doubled.

It is not contended that the linear form cannot exist but that it may

not exist. This does not imply that the linearity assumption should be

wholly discredited and discarded, but that there should be an awareness of

its implications. The linear form has considerable utility as a simplified




78





approximation where analysis would not be possible, or extremely difficult;

or where accuracy may be sacrificed for otherwise unavailable information.

The above discussion was undertaken mainly because accounting litera-

ture is completely devoid of any mention of such peculiarities. Most of

what has been written on the subject can be labelled as simple propaganda

that attempts to paint a rosy picture of how all the accountant has to do

is "collect" two pieces of production data, and use logarithmic graph paper

to draw a straight line experience curve, as some kind of a simple cure-all.

To reiterate, it is not contended that the linearity assumption is useless,

for it has a function to perform. It can be accepted as an approximation

for purposes of simplicity, only when its peculiarities are properly under-

stood.











FOOTNOTES
Chapter II


1. M. A. Reguero, An Economic Study of the Airframe Industry,
Air Materiel Command, Wright-Patterson Airforce Base (Dayton, Ohio:
October, 1957), p. 213.

2. Ibid.

3. T. P. Wright, "Factors Affecting the Cost of Airplanes,"
Journal of the Aeronautical Sciences, III (February, 1936), 122-128.

4. Ibid., pp. 124-125.

5. S. A. Billion, "Industrial Learning Curves and Forecasting,"
Management International Review, VI (1966), 68.

6. J. R. Crawford, "Learning Curve, Ship Curve, Ratios, Related
Data," (Burbank, California: Lockheed Aircraft Corporation, n.d.).

7. H. Asher, Cost-Quantity Relationships in the Airframe Indus-
try, R-291 (Santa Monica, California: The Rand Corporation, July 1, 1956),
pp. 15-46.

8. Publications by J. R. Crawford have been mentioned in the
Bibliography.

9. J. R. Crawford and E. Strauss, Crawford-Strauss Study, Air
Materiel Command (Dayton, Ohio: 1947). (Not reviewed by this study.

10. P. B. Crouse, "Projecting Labor Loads in Aircraft Produc-
tion," Aero Digest, XLIII, No. 4 (October, 1943), 216-218, 242-243.

11. A. B. Berghell, Production Engineering in the Aircraft In-
dustry (New York: McGraw-Hill Book Company, Inc., 1944), Chapter 12,
pp. 166-198.

12. K. A. Middleton, "Wartime Productivity Changes in the Air-
frame Industry," Monthly Labor Review, LXI, No. 2 (August, 1945), 215-225.

13. G. W. Carr, "Peacetime Cost Estimating Requires New Learning
Curves," Aviation, April, 1946, 76-77.

14. G. M. Giannini, "Aircraft Cost Control," Aero Digest, XXXIX
(August, 1941), 187-189.

15. P. Guibert, Mathematical Studies of Aircraft Construction,
Wright-Patterson Air Force Base, Dayton, Ohio. (Translation of P.
Guibert's Le Plan de Fabrication Aeronautique, Paris, 1945.) (Neither
reviewed by this study.)











16. E. Mensforth, "Airframe Production Part II," Aircraft
Production, IX, No. 108 (October, 1947), 388-395.

17. W. Z. Hirsch, "Firm Progress Ratios," Econometrica, XXIV
(April, 1956), 136-143; and "Manufacturing Progress Functions," The
Review of Economics and Statistics, XXXIX (May, 1952), 143-155.

18. F. S. Hoffman, Comments on the Modified Form of the Air-
craft Progress Function. RM-464 (Santa Monica, California: The Rand
Corporation, October 4, 1950.

19. A. A. Alchian, An Airframe Production Function, P-108 (Santa
Monica, California: The Rand Corporation, October 20, 1949); and Relia-
bility of Progress Curves in Airframe Production, RM-260-1 (Santa Monica,
California: The Rand Corporation, February 3, 1950).

20. Asher, op. cit., pp. 24-26

21. A. D. Searle, "Productivity Changes in Selected Wartime Ship-
building Programs," Monthly Labor Review, LXI (December, 1945), 1132-1147.

22. Reguero, op. cit., pp. 213-240.

23. Asher, op. cit., p. 191.

24. R. P. Zieke, "Progress Curve Analysis in the Aerospace In-
dustry," unpublished thesis, Stanford University, 1962, pp. 93-95.

25. F. J. Andress, "The Learning Curve as a Production Tool,"
Harvard Business Review XXXII (January-February, 1954), 87-88.

26. W. B. Hirschmann, "Profit from the Learning Curve," Harvard
Business Review, XLII (January-February, 1964), '125-139.

27. R. W. Conway and A. Schultz, "The Manufacturing Progress
Function," The Journal of Industrial Engineering, X (January-February,
1959), 39-54.

28. R. R. Cole, "Increasing Utilization of the Cost-Quantity Re-
lationship in Manufacturing," The Journal of Industrial Engineering, IX
(May-June, 1958), 173-177.

29. E. B. Cochran, "New Concepts of the Learning Curve,"The
Journal of Industrial Engineering, XI (July-August, 1960), 317-327.

30. Carr, op. cit., pp. 76-77.

31. E. C. Keachie, Manufacturing Cost Reduction through the
Curve of Natural Productivity Increase (Berkeley, California: Institute
of Business and Economic Research, University of California, 1964).











32. R. Wyer, "Industrial Accounting with the Learning Curve,"
The California C.P.A., XXIII (February, 1956), 24-30; "Learning Curve
Helps Figure Profits, Control Costs," N.A.C.A. Bulletin, XXXV, Sec. 1
(December, 1953), 490-502; "Learning Curve Techniques for Direct Labor
Management," N.A.A. Bulletin, XXXIX, Sec. 2 (July, 1958), 19-27.

33. R. Brenneck, "B-E Charts Reflecting Learning," N.A.A. Bulle-
tin, XL, Sec. 1 (June, 1959), 34; "The Learning Curve for Labor Hours -
For Pricing," N.A.A.Bulletin, XXXIX, Sec. 1 (June, 1958), 77-78; "Learn-
ing Curve Techniques for More Profitable Contracts," N.A.A.Bulletin, XL,
Sec. 1 (July, 1959), 59-69.

34. R. B. Jordan, "Learning How to Use the Learning Curve,"
N.A.A. Bulletin, XXXIX, Sec. 1 (January, 1958), 27-39; "What's Your
Progress Curve?" N.A.A. Bulletin, XLIII, Sec. 1 (March, 1962), 91-92.

35. B. T. Sanders and E. E. Blystone, "The Progress Curve--An
Aid to Decision-Making," N.A.A.Bulletin, XLII, Sec. 1 (July, 1961),
81-86.

36. V. J. Shroad, "Control of Labor Costs Through the Use of
Learning Curves," N.A.A.Bulletin, XLVI, Sec. 1 (October, 1964), 15-20.

37. A. E. Burrow, "Use of Learning Curves in Contract Audits,"
The GAO Review (Winter, 1967), pp. 35-46.

38. Others have been mentioned by H. Asher, op. cit., pp. 34-38.

39. T. F. Fowlkes, Aircraft Cost Curves: Derivation, Analysis
Projection (Re-issue, Fort Worth: General Dynamics, August, 1963), p. 52.

40. The Rand Corporation studies, conducted for the United States
Air Force, include: R-291, H. Asher, Cost-Quantity Relationships in the
Airframe Industry, July 1, 1956, 191pp; P-108, A. Alchian, An Airframe
Production Function, October 20, 1949, 16pp.; P-267, D. Novick, Use of
the Learning Curve, November 9, 1951, 6p.; RM-456, K. J. Arrow, S. S.
Arrow, Methodological Problems in Airframe Cost Performance Studies,
September 20, 1950; RM-464, F. S. Hoffmann, Comments on the Modified
Form of the Aircraft Progress Function, October 4, 1950, 12pp.; RM-260-1,
A. Alchian, Reliability of Progress Curves in Airframe Production, Feb-
ruary 3, 1950, 30pp.; RM-536, K. J. Arrow, S. Arrow, and H. Bradley,
Cost Quality Relations in Bomber Airplanes, February 6, 1951.

41. Included in the Stanford Research Institute Studies are:
Development of Production Acceleration Curves for Airframes, September,
1948. Relationships for Determining the Optimum Expansibility of the
Elements of a Peacetime Aircraft Procurement Program, December, 1949.
A Method of Estimating Direct Operating and Maintenance Costs of Mili-
tary Transport Aircraft, June, 1954. (All attempts made by the author
to secure these studies for perusal were unsuccessful.)











42. Wright, op. cit., p. 124.

43. Ibid., pp. 124-125.

44. R. B. Jordan, "What's Your Progress Curve?" N.A.A.Bulletin,
XLIII, Sec. 1 (March, 1962), 91-92.

45. Crawford, Learning Curve, Ship Curve, Ratios, Related Data,
as reported by Asher, op. cit., pp. 21-24.

46. H. R. Krockcr and R. Peterson, "A Handbook of Learning Curve
Techniques," The Ohio State University Research Foundation (Columbus,
Ohio: 1961), p. 21.

47. Alchian, An Airframe Production Function, p. 4.

48. A. Alchian, Reliability of Progress Curves in Airframe Pro-
duction, p. 30.

49. Ibid., pp. 10-11.

50. Cole, op. cit., pp. 174-175.

51. P. F. Williams, "The Application of Manufacturing Improve-
ment Curves in Multi-Product Industries," The Journal of Industrial
Engineering, XII (March-April, 1961), 108.

52. D. Schreiner, "The Manufacturing Progress Function: Its
Application to Operations at IBM, Endicott," unpublished paper presented
on behalf of International Business Machines Corporation.

53. E. C. Keachie, op. cit., p. 83.

54. Hirschmann, op. cit., pp. 125-139.

55. J. H. Siersema, "The Learning Curve," Cost and Management
(May, 1960), pp. 186-200.

56. Letter dated September 26, 1967.

57. J. A. McGeoch and A. L. Irion, The Psychology of Human Learn-
ing (New York: David McKay Company, Inc., December, 1961), pp. 1-34.

58. Ibid.

59. Ibid., pp. 26-27.

60. L. A. Barron, "Learner Curves Boost Team Output," American
Mechanist, CII (December 1, 1958), 100.












61. F. J. Powers, "Costs Strike Out with Learning Curve Incen-
tive," Factory (October, 1961), 90.

62. J. R. Hadley, "Learning Curves on Log-Log Paper," Advanced
Management, XV (April, 1950), 16-17.

63. L. Wertman, "Putting Learning Curves to Work," The Tool
Engineer, XLI (September, 1959), 100-101.

64. For details on the choice of a term to signify the business
"learning curve," refer to Y. Bhada, "The Experience Curve," unpublished
master's thesis, Bowling Green State University, August, 1965.

65. A set of data concerning a linear unit hour pattern has
been used in this example for purposes of simplicity. The cumulative
average hours could be used in place of the unit hours, without affect-
ing the analysis.

66. For a good treatment of the subject, refer to Krocker and
Peterson, op. cit., pp. 4-7.

67. A sample of semi-logarithmic paper can be seen on p.

68. For the remainder of this study, it will be referred to as
logarithmic paper.

69. Krocker and Peterson, op. cit., pp. 6-7.

70. A. A. Alchian, "Costs and Outputs," The Allocation of
Economic Resources, M. Abramovitz, et al. (California: Stanford Univer-
sity Press, 1959), pp. 23-40.

71. B. I. Maynard, "Mathematical Theory of Time Reduction Curves,"
Proceedings of the Fifth Annual Industrial Engineering Institute (Univer-
sity of California, 1953), p. 31.

72. Wright, op. cit., pp. 124-125.

73. Crawford, op. cit.

74. Krocker and Peterson, op. cit., p. 58.

75. Carr, op. cit., pp. 76-77.

76. Wright, op. cit., pp. 122-128.

77. Conway and Schultz, op. cit., pp. 39-54.




84






78. Relationships for Determining the Optimum Expansibility of
the Elements of a Peacetime Aircraft Procurement Program, S.R.I., pre-
pared for the Air Materiel Command, United States Air Force (December
31, 1949), as reported by Asher, op. cit., pp. 43-45.

79. Costs of distribution, general administration, etc., have
been left out of the analysis in order to make the example simple to
comprehend. Their inclusion would not affect the analysis in any sig-
nificant manner.

80. Asher, op. cit., p. 72.

81. Cochran, op. cit., pp. 319-321.

82. R. M. Barnes, J. S. Perkins, and J. M. Juran, "A Study of
the Effects of Practice on the Elements of a Factory Operation," Uni-
versity of Iowa Studies in Engineering, Bulletin 22 (November, 1940),
pp. 3-86.











CHAPTER III

PROJECTING DYNAMIC PRODUCTION DATA


Purpose and Organization of the Chapter


What is the role of an accountant in the proper accumulation and

dissemination of production data? How can accounting analyses concerning

an entity be undertaken so that the impact of quantity produced on costs

or production time be given adequate recognition? Partial answers to these

questions have been attempted in the next few pages.

Before any analyses can be conducted on the implications of experi-

ence gained on the quantity produced, it is essential to know how account-

ing data can be recorded, accumulated, and classified, for it is on the re-

liability of the data presented that interpretations and judgments are

based. The importance of managerial accounting depends on the accountant's

analytical judgment which, in turn, is based on his knowledge, experience,

and the reliability of data available to him. For these reasons, it is ex-

tremely important to know the proper means of accumulating data and arrang-

ing the information in a manner susceptible to adequate analysis and re-

liable interpretations.

With this in mind, the first section of the chapter has been aimed

toward indicating what dynamic production data implies and the proper means

of accumulating such data. Special emphasis has been placed on the varied

difficulties that may be encountered in the process of accumulation, and

possible treatments for such difficulties have been indicated.











The second section contains an exhaustive treatment of the possible

patterns that have been and can be observed in dynamic production data pro-

jections. The varied forms have been illustrated with graphs, tables, and

mathematical formulae wherever possible. Suggestions for the study of con-

tinuous production data, which have utilized variables other than the con-

ventional variables--cost, production time, and cumulative quantity produced--

have been commented on in the last section.

It is necessary that the accumulator of accounting information be

aware of the different possibilities in order to be able to adapt to dif-

ferent situations. For accounting information to be valuable, it has to be

relevant, and the principle of relevancy can be satisfied only if all the

possible alternatives are known. Presenting the alternatives is what has

been attempted in these last two sections.


Accumulation of Accounting Data

The dearth of literature on the subject of ascertaining the proper

means for collecting dynamic production data is almost unbelievable. Most

publications advocating the use of production time-quantity relationships

prefer to side-step the issue with an implied assumption regarding the

availability of relevant production information. Only a few references

touch on the procedure for accumulating data, and fewer still point out

the difficulties that may be encountered. For this reason, a detailed in-

vestigation of these aspects has been undertaken in this section.

The recording and accumulation of financial or quantitative data

which can be utilized for discerning progress trends are undoubtedly within

the realm of an accountant's job. The duty of collecting relevant informa-











tion should fall squarely on the shoulders of the accountant, to whom the

task of gathering data on production time or costs is by no means a new

duty. Whether an accountant should be proficient enough in the use of

sophisticated statistical and mathematical tools, or should these details

be left to other "specialists" such as the industrial engineer is a debat-

able question. However, there is no doubt that the responsibility for ac-

cumulating the relevant details should be placed in the hands of the cost

accountant.

What should be the proper procedure for dynamic data collection?

The usual simplified answer, implied by most authors, has been used as the

starting point to lead into a discussion on the difficulties encountered in

the process of accumulation.

In the first place, determine whether the product or firm is sus-

ceptible to the impact of experience. In other words, is the nature of

the manufacturing process such that the effect of experience gained with

increased production could significantly affect the production time or cost

of subsequent units produced? The implication is that if, for a firm or a

product, the reply is negative, one can forget about the effects of experi-

ence, and use conventional accounting procedures. However, what is not in-

dicated is that an answer to the above question cannot be supplied unless

and until a thorough investigation has been undertaken to determine the

impact of experience. It would be difficult to attempt an a priori judg-

ment on whether the implications of experience are significant for inclu-

sion in accounting analyses.

For example, Frank Andress listed five industries, the products of










which could profitably utilize the experience curve, and noted that a

priori, a few other industries would find the implications of experience

"of little value." This latter group included basic chemicals, plastics,

petroleum refining, and manufacture of certain kinds of standard toys.

Andress' claim was strongly refuted by Winfred Hirschmann, who presented

empirical findings to support the contention that the effect of experience

could be definitely observed in all the products and processes listed by

Andress in his "of little value" group.2 Some form of an empirical inves-

tigation must be undertaken to ascertain whether a production process gene-

rates experience which could affect data used for decision making.

The next step advocated is to obtain the relevant data and make the

necessary calculations. This is easier said than done; and yet, how many

references can be quoted which merely state this requirement, and then go

on to explain routine applications, assuming availability of accurate data.

nhat exactly is "data"? How can its relevancy be ascertained? How

does one go about obtaining this all-important ingredient? A composite

answer to these questions usually implied is to determine the labor hours

or the cost per unit as production takes place, and plot these data on

logarithmic graph paper.

In the first place, it would be important to define the "unit of

production." In most cases, this would not be a difficult problem, for the

unit of output may be readily identifiable. However, several problems of

identification can, and do, arise. One such practical difficulty that has

been observed pertains to the determination of the status of a product.

Can a product, on which production has started, be considered new, or is










it merely a variation of a product manufactured previously? This author's

experience may be pertinent in illustrating the problem.

An order was received from a major tire manufacturer for assembling

a certain quantity of a special truck body. The customer indicated several

specifications and details for assembly to the engineering department of

the body construction company. However, similar units were being assembled

at that very time for another tire manufacturer and although there were

several variations between the two assemblies, there were considerable

areas which were almost identical. The assembly crews that had worked on

the earlier assembly were also to work on the new body, but with a few new

workers introduced into the crews. The question that arose was, should the

new order be considered as a continuation of production or be treated as a

new product?

In a situation such as this, the accountant would have to seek the

opinion of the industrial engineer or some other specialist who has a better

knowledge of the production process. In the above situation opinions were

divided between the production manager, industrial engineer, the engineering

department, and the shop foremen. The intensity of the problem was such

that no decision could be made for purposes of considering the dynamic

relationship.

A corollary of the above problem is another knotty situation. Which

unit should be considered as the first unit produced? In some cases proto-

types might have been built, or sample batches manufactured. Should these

be considered as units produced, or should they be left out of the analyses?

In most cases, prototypes or sample batches are produced with the











help of special processes which are usually different from the production

processes used in regular production. If such be the case, experience

gained in their production may be left out of analyses. However, the in-

clusion or exclusion would have to depend upon the particular circumstances,

and the criterion of relevancy would have to be utilized.

Another case which is conceivable is where production of a few units

might have been scattered over a long period of time. For example, one unit

might have been produced six months back, another unit four months earlier,

a third unit only a month ago. Should these be considered as units pro-

duced, or should the unit under present construction be considered as the

first unit? Once more the answer would have to be determined under the con-

cept of relevancy, depending upon the degree to which transfer of experience

could take place between the units produced.

Yet another problem is encountered with partially completed units

which might be in inventory. Here, the accountant's equivalent units con-

cept can be profitably employed. However, what about fully or partially

completed units which are rejected or are to be scrapped. To the extent

that these units and the requisition of experience, they should be recog-

nized adapting conventional procedures used, such as those for process cost

accounting. If the output consists of joint products, conventional ac-

counting treatment could once again be applied for calculation of units

produced.

Regarding labor hours or costs, it should be noted at the very out-

set that reference is to actual amounts observed, and not to any estimated

figures. The danger in using estimated amounts is extreme, and such figures











can be used only as rough approximations, and only if the user is completely

aware of the dangers involved.

Often, it might not be possible to identify actual labor hours with

individual units produced. For example, in the case of multi-product manu-

facture, total labor hours or costs may be collected for batches or lots of

several units, in which case only an average can be used to identify the

labor hours expended on each unit in the lot. In such cases, lot aver-
3
ages can be used instead of individual hours for each specific unit.

Ascertaining the unit labor hours, or the costs per unit, could pre-

sent several difficulties. Considering the problem of labor hours first, an

initial problem might arise in the differentiation of direct labor from in-

direct labor used. Although normal accounting definitions can be utilized

to differentiate between the two categories, the validity of times charged

to direct or indirect labor would always be questionable. However, once

again conventional accounting definitions can be utilized, with minor vari-

ations, if necessary.

Rolfe Wyer illustrates the difficulties involved in the accumulation

of direct labor hours with examples regarding three cost elements: machine

set-up, production inspection, and process operations.4 His point is that

accountants often include these items under direct labor hours; and although

each element might involve experience, there are certain characteristics

which can significantly affect analyses if proper care is not taken. For

example, where inspection is concerned, 100 per cent inspection might be

undertaken for the first few items; whereas, only about 5 per cent inspec-

tion might take place nearing the end of the production run.5 This may












indicate a completely different rate from other constituents, such as as-

sembly labor, and hence its inclusion might introduce instability in the

data.

Another major problem is that of "attaching costs." If a job order

cost system is in effect, the process of accumulating costs of assembly

might not prove difficult, for a job order sheet could accompany each unit

or lot as it passed through the different assembly operations. However, the

question of machined parts is quite different. Some of the parts used for

assembly purposes might be bought from outside, others might be produced at

the plant, still others might be partially worked on or assembled in the shop.

Should the time spent in the shop be included in the total labor hours figure

or should machining be looked upon as a separate operations and costs separ-

ately collected? This question could arise provided the hours can be direct-

ly allocated to the units. But in most production situations, varying lot

sizes, varying lead times, and varying schedules make it difficult to asso-

ciate specific production quantities with the end product. Some components

may be produced in relatively large quantities in initial lots, or lots may

be split in the process of production. Some parts may be produced in the

shop initially, and bought from outside suppliers later on. How should

these problems be dealt with by the accountant?

Two solutions to this problem of aggregation have been supplied by

Conway and Schultz. One method is to time phase the data and add all the

values making up a specific accumulation of the finished product. Another

alternative is to accumulate each item cost at its cumulated production, and

arrive at the total labor hours through simple aggregation of each unit of

production.




Full Text

PAGE 1

SOME IMPLICATIONS OF THE EXPERIENCE FACTOR FOR MANAGERIAL ACCOUNTING By YEZDI BHADA A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PAKTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA

PAGE 2

3,,,iiiiiiiiiii 3 1262 08552 3974

PAGE 4

ACKNOTviLEDGMENTS The author wishes to express his indebtedness to all those who have assisted him in achieving his goals, including his supervisory comnittee members: Dr. John H. James, Dr. Ralph H. Blodgett, Dr. Charles W. Fristoe, and Dr. Williard E. Stone. He is especially grateful to Dr. James W. Davault, committee chairman, whose patience and guidance were most encouraging. Gratitude must also be expressed to Dr. Harvey E. Donley, Professor of Accounting, Bovjling Green State University, for his role in getting the author interested in the subject of this dissertation. Above all, he would like to express his gratitude to his wonderful wife, Perviz, who preferred to sacrifice a life of security and comfort to follow the man in whom, she had faith. Patiently has she endured years of hardship and loneliness, an accomplishment for which he bows his head in true respect. Finally, he wishes to express his admiration for this wonderful land of opportunity. God bless America, and all those who have m.ade it the great nation it is.

PAGE 5

TABLE OF CONTENTS ACKNOWLEDGMENTS ii LIST OF TABLES v LIST OF FIGURES vi CHAPTER I INTRODUCTION 1 Nature and Scope of the Study 1 Definitions of Key Terms 21 Research Methodology Employed 26 Organization of the Remainder of This Study 29 II EXPRESSING THE DYNAMIC RELATIONSHIP BETVJEEN COST OR PRODUCTION TIME AND THE QUANTITY PRODUCED 35 Purpose and Organization of the Chapter 35 A Historical Sketch of Contributions to the Establishment of a Cost-Quantity Relationship 36 Development of the Linear Logarithmic Dynamic Cost Function 42 The Learning Curve 46 A Critique of the Conceptual Implications of Experience Curve "Theories" 64 III PROJECTING DYNAMIC PRODUCTION DATA 85 Purpose and Organization of the Chapter 85 Accumulation of Accounting Data 86 Possible Patterns in Dynamic Production Data Projections 96 Variations Suggested for the Study of Dynamic Data. . 128 IV QUANTITATIVE AND QUALITATIVE IMPLICATIONS OF THE EXPERIENCE RATE 133 The Purpose and Organization of the Chapter 133 Statistical and Mathematical Implications 134 The Experience Rate and the Slope of the Experience Curve 160 Significance of the Experience Rate 171 Factors Influencing the Experience Rate 176 V SPECIFIC IMPLICATIONS FOR MANAGERIAL ACCOUNTING \. '. . . 192

PAGE 6

TABLE OF CONTENTS (continued) V The Purpose and Organization of the Chapter 192 Implications for Costing 193 Implications for Planning 215 Implications for Control 234 VI SUMMARY AND CONCLUSIONS 262 APPENDICES A OTHER TERMS USED IN PLACE OF, OR IN REFERENCE TO, THE EXPERIENCE CURVE 278 B UNIT HOUR FORMULA MODIFIED FOR DESIGN CHANGES AS SUGGESTED BY GARG AND MILLBIAN 280 C DERIVING THE LOGARITHICLC LINE OF BEST FIT USING THE METHOD OF LEAST SQUARES 281 BIBLIOGRAPHY 284 BIOGRAPHICAL SKETCH 295

PAGE 7

LIST OF TABLES TABLE PAGE II-I Selected Values from an Hypothetical Cumulative Production Schedule 55 II-II Selected Cost Data for Product X 67 II-III Cost Data Signifying Constant Rate of Decline for Tripled Quantities 74 III-I Production Data Indicating a Constant Rate of Improvem.ent for Unit Hours 98 III-II Production Data Indicating an Initially Fast Rate of Improvement for Unit Hours 101 III-III Production Data for Units Produced in Identifiable Lots 106 III-IV Production Data Indicating a Constant Rate of Improvement for Equal Quantities Produced 115 III-V Production Data Indicating No Apparent Trend, Before and After Reclassification 125 IV-I Assembly-Time Analysis for the First Nineteen Units Produced 142 IV-II Assembly-Time Analysis for the Next Twenty-Five Units Produced 151 IV-III Slope Coefficients, Conversion Factors, and Angles of Decline, for a Range of Experience Rates 166 IV-IV Relationship Between Manual-Mechanical Ratios and Experience Rates for Four Industries 174 IV-V Relationship Between Manual-Mechanical Ratios and Their Corresponding Experience Rates for Various Operations 174 V-I The Effect of Declining Cost Per Unit on Resultant Profit 205 V-II Production Cost Analysis with and without Consideration Given to the Experience Factor 212 V-III Relationship Between Increases in Quantatives Ordered and Their Resultant Prices 228 V

PAGE 8

LIST OF FIGURES FIGURE PAGE I-l Long Run Production Time Declines Experienced in Two Industries 6 II-l Representative "Learning Curves" As Used for Psychological Analyses 49 II-2 An Actual Learning Curve Derived in a Psychological Experiment 51 II-3 An Example of a "Learning Curve" Used for an Incentive Wage Pajmient Scheme 52 II-4 Graphical Representation of Initial Cumulative Production Data on Arithmetic-Grids 56 II-5 Graphical Representation on ArithmeticGrids After a Substantial Level of Production Has Been Achieved ... 58 II-6 Hypothetical Data (from Table 1) Plotted on Logarithmic-Grid Graph Paper 60 II-7 Effect of Different Improvement Rates for Cost Elements on the Total Cost Projection 69 II-8 Effect of Linear Component Curves of Different Slopes on the Unit Curve 71 II-9 Constant Rate of Decline for Tripled Quantities As Projected on Logarithmic-Grids 75 III-l Constant Rate of Decline for Unit Labor Hours 99 III-2 Constant Rate of Decline for the Cumulative Average. . 103 III-3 A "Scalloped" Representation 107 III-4 Constant Rate of Decline for Lot Averages 108 III-5 A Humped Unit Hour Curve 110 III-6 An "Inverted S" Curve 113 III-7 Constant Rate of Decline for Equal Quantities, Projected on Full-Logarithmic Grids 117 vi

PAGE 9

LIST OF FIGURES (Continued) FIGURE PAGE III-8 Constant Rate of Decline for Equal Quantities, Projected on Semi -Logarithmic Grids 118 III-9 An Example of a "Leveling-Of f " Curve: Lockheed, Burbank--B 17 120 III-IO An Example of a "Toe-Up" Curve: Boeing Seattle, B 17 Learning Curve 121 III11 An Example of a "Toe-Doxm" Curve: Douglas, Tulsa B 24 Learning Curve 123 III-12 A No-Trend Projection 126 III13 Trend-Lines from Reclassified No-Trend Data 127 IV-1 Unit Hours from Table IV-1 Plotted on Arithmetic Grid Graph Paper 144 IV-2 Unit Hours from Table IV-1 Plotted on Logarithmic Grid Graph Paper 145 IV-3 "Raw" Trend on Logarithmic Grids 145 IV-4 A Linear Function Fitted to the Data from Table IV-1. . 147 IV-5 A Third Degree Polynomial Fitted to the Data from Table IV-1 149 IV-6 Figures I\'-4 Replotted with Data from Table IV-II Added to the Original Graph 152 IV-7 Straight Line Projections Using Different Points for Derivation of Trends 153 IV-8 Straight Line Projections Using Different Points for Derivation of Trends, As Applied to the Cumulative Average Plots 155 IV-9 Extrapolations of Trends Indicated in Figure IV-8 for Large Quantities 157 IV-10 Unit Hours from Tables IV-I and IV-II Plotted on Plain Graph Paper with Trends Indicated Using Polynomials . . 158

PAGE 10

LIST OF FIGURES (Continued) FIGURE PAGE IV-11 Trends Fitted to Satisfy One Version of the "Experience Curve Theory" 161 IV-12 Trends Fitted to Satisfy the Other Version of the "Experience Curve Theory" 162 iy-13 Derivation of the Slope Coefficient 164 V-1 Comparison of Break-Even Points 214 V-2 Usage of Constant Times, Compared with Declining Time Per Unit for Labor Requirement Forecasting 219 V-3 Comparing Effectiveness of Two Control Lines on a Set of Data Plotted on Plain Graph Paper 238 V-4 Comparing Effectiveness of Two Control Lines on a Set of Data Plotted on Logarithmic Grid Graph Paper .... 239 V-5 An Example of Control Through the Use of Declining Trends 242 V-6 An Example of Control with the Aid of Confidence Limits. 245 V-7 Effect of Declining Production Time on Variance Analysis 250 V-8 Influence of Worker-Learning on Productivity 256 viii

PAGE 11

CHAPTER I INTRODUCTION The purpose of this chapter is to give the reader an idea regarding the subject matter of the study. Specifically, to express the nature and limitations of the work undertaken, to state the involved hypotheses, to define certain key terms, to throw light on the methodology used, and to outline the study in general. Special care has been taken to substantiate assumptions accepted, and to differentiate the work undertaken by this study from apparently similar research conducted under the aegis of various disciplines. That the study has been made from a managerial accountant's point of view has been emphasized, and a generalized indication of what this involves has been attempted. Nature and Scope of the Study Recognition of the phenomenon of experience The hypothesis that an organism improves its effectiveness, or, in other words, "progresses," m.ay be validated without detailed investigation by means of everyday observations, or V7ith the help of simple scientifically controlled experiments. Those who appreciate a less rigorous approach might be tem.pted to consider the hypothesis as "evident," on the ground that one im.proves as one partakes in the events of existence; and given a sufficient period of time, one is bound to become more efficient, especially in cases which involve repetitive operations.

PAGE 12

For the purpose of research, the above hypoto.esiS has been accepted, but not on a priori grounds. Several studies have been made.. ranging from experimentation with individuals as subjects under simulated conditions, to ex-post observations involving entire industries functioning under normal conditions. Almost all the references listed in the bibliography substantiate the hypothesis in one way or another. However, an investigation might be in order. Historical data furnish a reliable starting point to serve as evidence of the existence of improvement as a product of experience. The human race has come a long way since the time man sustained his physiological needs by trying to kill his anim.al adversaries with the help of bare hands. It was not long before man "learned" that the task could be accomplished much m.ore efficiently by creating special equipment. He even found that he could optimize his situation by bartering his surpluses in order to receive scarce goods in return. With time he learned to do several new operations and to perform various functions more efficiently, until finally he arrived into the age of trade and commerce, and was soon engulfed by the industrial revolution. The need for increased production led to the introduction of more efficient capital equipment, and the rate at which obsolescence began to be recognized for otherwise productive equipment was continuously increasing. In other words, man was developing his effectiveness through the experience he had gained in the process of living. Even the tenets of "scientific management" ushered in by Frederick Taylor and others depended to a considerable degree on the implied assum.ption of "experience" and

PAGE 13

improvement. Today, more than ever before, increases in productiveness and efficiency can be witnessed in almost every walk of life, and the age old adage "experience is the best teacher" is as widely accepted today as it was several decades ago. The causes of improvements, and the reasons for the existence of experience, are varied. Several psychological theories have been formulated, each of which may be questionable as to its assumptions, implications, and solutions. However, there can be little disagreement regarding the acceptance of improvement as a phenomenon which can be witnessed, and which can considerably influence life on our planet. There might be a question of degree involved, for in some cases there might be more opportunities for improvement than in others; however, it can be safely generalized that, given sufficient time, experience will affect efficiency, Can we extend the above hypothesis regarding the phenomenon of experience to business and industrial situations? The answer is an emphatic affirmative. There are several reasons for accepting the applicability of the hypothesis to manufacturing situations. In the first place, there would be the added factor of a concerted effort toward greater efficiency due to the element of competition in the business world. This statement can again be validated by observing existential data. Microeconomic theory implies an assumption, which can be used to support the contention that in a competitive economy there has to be a tendency toward optimization of efficiency, otherwise competition may force the firm, or even the industry, out of business. Moreover, production generally involves repetitive operations, and

PAGE 14

one may be safe in generalizing that there is ample opportunity for gaining experience at performing a function more efficiently. Under such conditions the probability of grasping operations in terms of their essentials is certainly high; and improvement through experience gained is more likely. As stated earlier, to verify the applicability of the hypothesis to business situations, one merely has to collect the necessary data for a product, process, firm, industry, or even an economy. Almost all references cited in the bibliography involve some element of empirical investigation to support the hypothesis. To illustrate, a few selected studies are mentioned below. A team of researchers at the University of Iowa investigated the effect of learning on individuals at performing a punch-press operation 2 under laboratory conditions. The task was broken dovTi into several suboperations (referred to as "therbligs"), and the effect of work-repetition on each of the therbligs was also studied. The results indicated that although the rates of learning differed between individuals, and even between different therbligs for the same individuals, there was a marked learning pattern for each operator for the task as a whole. A number of such simulated studies have been undertaken at universities and research foundations, mainly conducted to aid psychological experiments, most of which conclude with identical results. Several citations can be made for experience affecting the production of individual products, processes, and firms. For example, Werner Z. Hirsch investigated the effects of the experience factor on eight products

PAGE 15

3 and found a rate of improvement in all cases. In an article published in another journal, Hirsch states: "Concerning the direction of the slopes [of his plotted data] great consistency in the results was revealed. In all cases the progress function had a significantly negative slope. Other studies, taking into consideration entire industries, may be noted. The Monthly Labor Review p ublished a study undertaken by Allen D. 5 Searle to investigate production patterns in the shipbuilding industry. In this study, it was observed that man hours required declined for subsequent production of similar ships, in individual yards, and for the industry as a whole. In a similar type of study in the airframe industry, almost identical results were observed. Some rather interesting examples have been cited by Winfred B. Hirschmann on the long-term effects of improvement in specific industries. Figure 1 indicates the effect of continuous production on two major U. S. industries: petroleum and basic steel. Similar patterns could be derived for several other industries such as automobile, electric power, airframe manufacture, and building construction. One might even generalize that if data were properly adjusted, similar patterns might be observed for any and every type of production facility. One has merely to consider the regulations imposed by various governmental agencies and other organizations regarding the utilization of the concept to realize that not only is it recognized, but it is considered extremely valuable. For example, the National Aeronautics and Space Administration makes it obligatory for a contractor to consider the effect Q of experience for reporting costs. A handbook has also been issued by

PAGE 16

1.5 1.0 0.8 0.6 0.5 0.4 0.3 0.2 0.1 .08 .06 Per Barrel Refined in the Petroleum Indust

PAGE 17

NASA which presents guidelines and instructions for preparing necessaryforms, including Form 534a, on the preparation of the "Contract Progress 9 Curve Report." The General Accounting Office, the Defence Contract Audit Agency, etc., have also issued detailed instructions on the usage In conclusion, it may be reiterated that experience does affect operations; and although the rate at which it affects different functions may vary, its extence can be validated without serious difficulty. Experience as studied by various disciplines Philosophers, psychologists, management scientists, economists, engineers, and others have all faced the implications of experience upon their particular areas of interest. Undoubtedly, each discipline has looked upon the significance of experience from its own subject-matter point of view, and each has tried to answer different questions. It might be pertinent to review briefly the types of questions posed, and answers sought by each of these disciplines. If one were to ask the question "what is philosophy," a variety of replies might ensue, with perhaps no two answers being the same. Professor Levi indicates that, at the very most, one could say, "It is the activity of serious and able men reflecting upon, meditating, reasoning about, and considering deeply the nature of their experience. . . . All philosophy begins with experience." In other xsrords philosophy has no subject matter of its o\m., but draws its material from experience itself. It tries to formulate theories which can be processed to enhance human understanding and knowledge which

PAGE 18

could then be utilized for ordering human life in a more efficient manner. The interest of philosophers is centered around experience as it affects human existence, and not minor events. Different philosophers have arrived at different conclusions depending upon their particular points of view. Thus, the empiricists such as John Locke, A. J. Ayer, and Bertrand Russell have considered the implications of experience differently than have the pragmatists such as John Dewey, Charles Pierce, and P. W. Bridgem.an. An investigation into the details of various views presented by the philosophers would be a digression beyond the scope of this study, and hence it may suffice to say that the study of experience as undertaken by students of philosophy may be considered as being of a different nature and scope than that undertaken in this research. The amount of research done by psychologists in the area of learning needs little introduction. The main questions posed by the psychologists are: "U^hy does learning take place? How do people learn? and what can be done to improve the rate of learning in individuals?" They have long recognized that modes of perceiving are functions of past experience, which is another way of saying that they are products of learning; and knowledge of the characteristics and the conditions which determine the occurrence of learning is fundamental to an understanding of psychological development and organization. The first two paragraphs from Prof essors Hilgard and Bowers' book on the Theories of Learning are interesting enough to be quoted in full:

PAGE 19

The study of learning is shared by many disciplines. Physiologists, biochemists, and biophysicists have a legitimate interest in it; parents, teachers, industrial managers, rehabilitation workers, and others faced by the practical problems of the control of learning have their own needs which require that they understand the basic processes and how to manage them. Yet the scientific study of learning is carried on primarily by psychologists. Psychology's claim to the field was staked out in part by masterly pioneers such as Ebbinghaus (1885) and Thorndike (1898). Those who have followed in their footsteps have been primarily psychologists. Professional educators have welcomed educational psychology as a foundation science upon which to build their practices, and studies of learning have gone on concurrently in laboratories of general psychology and laboratories of educational psychology, with interplay between the pure and applied fields. Under the circumstances, it is very natural for psychologists to feel that the study of learning belongs to them. In addition to historical reasons, there is another basis on which to account for the psychologist's interest in learning. This is the centrality of learning in the more general systems of psychological theory. A scientist, along with the desire to satisfy his curiosity about the facts of nature, has a predilection for ordering his facts into systems of laws and theories. He is interested not only in verified facts and relationships, but neat and parsimonious ways of summarizing these facts. Psychologists with a penchant for systems find a theory of learning essential because so much of man's diverse behavior is the result of learning. If the rich diversity of behavior is to understand in accordance with a few principles, it is evident that some of these principles will have to do with the However, the psychologists' "claim to the field" has been mainly in the area of trying to understand the reasons for the occurrence of learning, where and how it can be embodied, and finding ways and means of Stimulating the rate of learning. Above all, the science of psychology deals primarily with the individual as a unit, and group behavior or interactions encountered in business organization is beyond the scope of its study. Various theories have been offered as explanations for the existence of learning. Hilgard and Bower supply a detailed reference to some of the

PAGE 20

10 more important ones, including those of Edward L. Thorndike, Ivan Parlov, Edwin R. Guthrie, B. F. Skinner, Clark L. Hill, Edward C. Tolman, Sigr'und Freud, and other prominent psychologists .'•^ For a more concise treatment, the reader is referred to a series of three articles (of which Part I is the most pertinent) by Roger Bellows. Once more, it can be reiterated that the problems of learning and experience as viewed and investigated by the science of psychology are of a significantly different nature than the problems as viewed and investigated in this study. The differentiation is more clearly expressed further on in this chapter. A surprising amount of work has been done on the recognition of experience as a relevant phenomenon in the field of engineering, especially in the area of industrial engineering. Most of the early work on the experience factor was done by engineers, and the engineering departments of various airframe production plants were the first to recognize and deal effectively with the implications of experience. For example, T. P. Wright, the father of dynamic cost relationship analysis, noted its implications in his renoi;med article published in February, 1936, while connected with the engineering function of Curtiss-Wright Corporation. As would be expected, the engineer is more concerned with the effects of experience on his specifications, production scheduling, etc., and any im.plications which do not involve his mathem.atical calculations are disregarded as beyond the scope of his interest. Furthermore, most engineering studies involve highly complicated mathem.atical treatments, which may lie beyond the comprehension of other less sophisticated

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11 personnel. However, the science of engineering has contributed considerably to the proper measurement of experience, and has supplied tools for measurements which were not otherwise available. Professor A. B. Berghell's chapter on "learning curves" can still serve as an excellent reference for mathematical calculations regarding quantification of the experience factor. It may be noted that there are several areas of similarity between the nature of engineering studies and the work undertaken in this study; hox^7ever, the significant difference is in the scope of the studies. As previously stated, the engineering studies are merely concerned with specific applications to peculiar engineering models and problems. The present study is more concerned with the implications from the standpoint of managerial accounting. An excellent exam.ple of an engineer's interest in the implications of experience is evidenced in a study made by Kenneth Hammer for a thesis submitted to Cornell University as requirement for the 20 degree of Master of Science. Equally surprising is the allegation that not much work has been 21 done on the implications of experience ir. the field of economics. It should be noted that the experience factor (as defined later) is concerned with what would be considered in economics as a "technological change." Hence, in traditional micro-economic analysis, the factor is assumed away in the construction of the static cost curves. The production function, as derived with the help of actual data using cumulative production and not rate of output, may be considered a dynamic function, and hence cannot be compared to the traditional micro-economic

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12 static cost model. An attempt was m.ade by W. Z. Hirch to reconcile the traditional cost curves to the dynamic production functions obtained by using cum.ulative production. The follov/ing quotation has been reproduced in order to clarify any ambiguity that may exist regarding economic cost functions and 22 those derived during the course of this study: Most economic cost studies have been concerned primarily with the relation of cost to rate of output. Shortrun costs are usually said to be those associated with variation in the utilization of fixed plant or other facilities, whereas longrun cost emcompasses changes in the size and kind of plant. Strictly then, the distinction is based upon the degree of adaptation of all input factors to rate of output. However, cost may vary because of changes in technical knowledge. Economists have explicitly excluded all irreversible changes in technology. Most longrun cost theories, for instance, are timeless; one future point in time is selected at which output rate and facilities are permitted to change. That such a cost function, particularly its height, will be affected by improvements in technical knowledge is beyond doubt. It is convenient to clarify the issue of the different cost functions by referring to production functions, which express the net relation between the input of variable productive factors and output during a given production period, under the assumption of a given plant and technical knowledge. From the production function we can derive a static shortrun cost function which also assumes a given plant and technical knowledge. Longrun cost permits changes in the size and kind of plant, but assumes stability in technical knowledge. Thus, a longrun cost function is related to points on different production functions, each point involving a different plant while using the same technical knowledge. There can be a cost function which permits changes in technical Icnowledge but not in plant and other facilities. In a sense this is a dynamic cost function. If direct labor is the cost we consider, we shall speak about a (unit) learning of progress function. This expresses the net relation between the amount of direct labor needed to produce one product-unit and the cumulative units produced in a given facility. The progress function thus permits us to estimate the amount of direct labor needed to manufacture the Nth unit, from N, the cumulative number of the product-unit. The function is related to a number of points on different production functions involving successive changes in technical knowledge in a given facility.

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13 In a study conducted a few years back, Harold Asher bemoaned the fact that hardly any consideration had been given to the implications of volume on cost in economic literature, and stated that in the course of his research only one pertinent reference was found, although he did con23 fess to a less than maximum attempt at locating references. The last decade or so has witnessed a few contributions, including those by Asher and Hirsch, which were mentioned above. Noteworthy, among others, have been those of Armen Alchian and Jack Hirshleifer. In a paper entitled "Costs and Outputs," Alchian presented several propositions, including one wherein he stressed the importance of anticipated volume along with the rate of output for economic analyses. Alchian' s comments instigated Hirschleifer to continue research in the same direction, and the 25 results of his study were published by The Journal of Business . Hirshleifer ' s review and development of Alchian' s conceptions are interesting to note, for an attempt has been made to reconcile classical economic theory with em.pirical observations. However, the temptation to delve into the stated implications for economic analyses has been subdued, for the topic is considered beyond the scope of the present study. Another field (if one can refer to it as such) in which some work has been accomplished regarding the im.plications of experience has been that of operations research. However, the major portion of work done in this area has been the adaptation of learning "theories" to business problems. In other words, the focal point of interest has been "how can the rate of learning be improved through providing incentives, etc." A few studies have been directed toward other problems, which might be

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14 considered in the realm of the accountant's interest, and these can be considered in relation to the next section,. A few other disciplines, including business management, quantitative analysis, iiiarkctl;T;, and purchasing', have rccop;nizcd the existence of experience as a factor to be taken into consideration, but the approaches used in these cases have not been very much different from those utilized by the field of accounting, as discussed in the next section. Differences, if any, may be attributed to varied emphasis and scope rather than the nature or subject-matter under investigation. Experience as viewed by the managerial accountant TsTio is a "managerial accountant?" T'-Tiat is "management accounting?" How does it differ from any other form of accounting? These and other pertinent questions might have to be answered before one can digress into further discussion on the subject for this section. As this study is not on the finer points of management accounting, it might be advisable to refer to some authority on the subject. A statement prepared by the research staff for the guidance of members of the committees on research planning and accounting development and issued by the National Association of Accountants may be considered such an authority. The Association has defined the term as accepted previously by the Anglo American Council on Productivity. Management Accountancy is the presentation of accounting information in such a way as to assist management in the creation of policy and in the day-to-day operation of an undertaking. The technique of accountancy is of extreme importance because it works in the most nearly universal medium available for the expression of facts, so that facts of great diversity

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15 can be represented in the same picture. It is not the production of these pictures that is a function of manageIn other words, imnageraent or managerial accounting is that phase of accounting which actively supplies cost and other financial information to management for more efficient planning, organization, and control — information relevant to "internal" matters which can help management in its task of decision-making. Although emphasis is on information of a quantitative nature, there are elements of qualitative judgment involved. Thus, along with reporting of relevant data, there is the responsibility for communication and interpretation of the results. In any management function such as establishing objectives, planning, organizing, directing, staffing, controlling, the decision-maker can benefit from the data provided by the management accountant. The definition quoted above distinguishes managerial accounting from "financial" accounting on the basis of active participation by the management accountant in aiding decision-making of an internal nature. It is not contended that managerial accounting is completely independent of financial accounting, or vice versa. There is a marked relationship between these areas; however, the differentiation is in the goals aimed at, and the means available to attain the goals. The managerial accountant can help in the function of planning by furnishing relevant data for costing, pricing, budgeting, forecasting cash and fund flows, determining proper product mixes, providing solutions to operate-or-lease problems, expansion-or-shutdo\m situations, make-or-buy decisions, capital investment decisions, and various other decisions

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16 needing special information. Proper control can be accomplished by setting proper job, or process, cost systems, by the setting of standards, comparison of actual costs with set standards, and actual costs with 27 budgeted figures, analyzing variances, etc. In all these areas, the accountant is interested in establishing as much accuracy in his reporting function as possible, taking cognizance of the constraints encountered in any particular situation. However, to formulate effective information, judgmental factors might be involved. This makes him dependent to a considerable degree on statistical tools, such as the "average," extrapolation of data obtained from actual operations, and other tools and methods normally used for planning and forecasting. Nov;, if experience is involved in a manufacturing situation, then it might affect the different tasks of costing, pricing, etc. and the effect might be significant enough to introduce an element of ineffectiveness in the task of the managerial accountant. For example, the cost of direct material and direct labor is usually considered as fixed per unit of product. Thus, if one finds the prime cost of unit A to be $5, the prime cost of unit X is also assumed to be $5, irrespective of whether X is the hundredth or the thousandth unit. However, if the experience factor is taken into consideration, it might be found that the prime cost of unit X is not $5, but less. This might be due to the factor of experience causing a more efficient usage of materials and labor in subsequent production, which in turn XTOuld lead to a lower cost per unit. The significance of the deviation can be understood if one considers the "average" prime cost as $5. In other words, all the hundred or thousand

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17 units might be costed at $5 per unit, whereas the final units might actually have only $2 of prime cost embodied in them. The point is that accounting calculations provide as accurate results as the statistical tools and data applied, and inaccuracies in accumulation of classification, or use of methods could generate significantly unreliable results. In other words, if it is found that experience is a relevant factor to be considered for managerial accounting purposes, the results obtained by taking it into consideration would be more accurate than those obtained when its implications are disregarded. Therefore, it can be stated that the managerial accountant is interested in the experience factor inasmuch as it affects his tools, techniques, methods, and concepts. He is not interested in why human beings learn, or the reasons for experience leading to improvement as the psychologist might be. Neither is he interested in how to improve the rate of gaining experience among individuals, other than how he can guide m.anagement in making decisions in a manner that may produce optimization of efficiency. He is certainly not interested in philosophizing regarding the production experience in a manner by which the world would benefit intellectually through the gaining of experience. (In a particularistic sense, he might be considered as "philosophizing," although not in the sense of the generally accepted meaning of philosophy.) His interest in experience for engineering specifications and complicated mathematical implications is purely incidental, and even if considered within his realm, would constitute only a minute area of interest. His interest in the economics of technological change may be considered as

PAGE 28

18 more akin to his o\m area; however, as the subject of the effect of experience on economic analysis deserves more attention than short comments, it can be looked upon as a specialized area of study. Accordingly it will be considered as beyond the scope of this research, not for reasons of irrelevancy, but merely to keep the study within manageable bounds. Again, the managerial accountant is interested in any phenomenon only as it affects his analysis. This factor of relevancy would dictate his interest in most matters connected with individual firms and their specific products rather than entire industries or the economy as a whole. For this reason, plus the fact that the study has to remain manageable, primary interest has been related to a consideration of experience as it affects products and firms, rather than long-run industry trends. In other words, industry growth curves or economy-wide projections have been considered beyond the scope of this study, and any comment in connection with these areas have been clearly noted. Similarly "learning patterns" among individuals or social groups, other than their indirect effects on business decision-making, would also have to be considered as beyond the scope of this study. The managerial accountant is primarily concerned with answers to questions such as : 1. How does the factor of experience affect managerial decisions? 2. I^Tnat can be done to incorporate the effects of experience in reporting to management? That is, how can these effects be related to the various tools, techniques, and concepts so that more reliable interpretations can be made from the data available? 3. What are the best means by which the effects of experience can be quantified and measured?

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19 4. Are the results obtained from using such quantifications more significant for management decision-making? 5. What are the limitations and dangers of the attempted incorporating of the effects of experience? 6. Are there generalizations which could be hypothesized? Or, on the other hand, how important are the special conditions connected with different situations? In short, the managerial accountant is only interested in the fact that experience does affect efficiency, which in turn affects his position as a member of the management team. If the effect of experience is significant, if it can be quantified or otherwise incorporated into his area, he can utilize such information for aiding management in the functions of planning, organizing, and control. He is not interested in the "theory behind" its occurrence, but only whether the phenomenon can be observed, quantified, and incorporated in his field for greater effectiveness in facilitating business decision-making. The iJurpose of the study The purpose of this study is to investigate the implications of experience on the various managerial accounting tools, techniques, and concepts. The intention is to determine the effects of experience, to find means of incorporating such effects fcr accumulation, dissemination, interpretation, and reporting of pertinent information to management for effective decision-making in the functions of planning, organizing, and controlling. Means of quantification and incorporation have been studied as to their applications and limitations, and evidence to support particular approaches sought. The task of the managerial accountant has been kept

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20 uppermost in mind while suggesting means and approaches. The effect of the experience factor on costing for manufacturing costs, including material, labor, and overhead, and of marketing and general administrative cost, has been looked into. Its effect on costvolume-profit relationships has been investigated. The setting of standards and standard costs incorporating the experience factor has been studied, and solutions for proper incorporation supplied. In other words, it is the intention of this study to bring the factor of experience to the attention of the accounting profession, which has neglected its implications to a significant extent. The truth is that one hardly finds any mention of the subject in conventional textbooks, and very little effort has been made to consider its effects on problem.atic accounting situations. The purpose of this study is to show the accounting profession that the experience factor can be quantified, that dynamic production data m.ay be applied for m.ore effective quantitative analyses, and that the results derived from taking the effect of continuous production into consideration might contribute significantly to their function. In other words, it has been indicated that it might not be advisable to disregard the implications of experience on judgments based on a priori assumption such as "too difficult to apply," or "insignificant in our case," without actually making a concerted attempt to determine its effects. Some tentative hypotheses of this study are: 1. 'D-.n.t '-xpf-rioncc is a factor which affects manufacturing situ/r.<:l' /,').-, ; 2. That this factor can be quantified and incorporated into accounting analysis;

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21 3. That the incorporation might involve more than the oversimplified linear logarithmic model popularized by the learning curve theory^? 4. That the effectiveness of managerial accounting can be enhanced by considering the factor of improvement; and 5. That failure to investigate its implications might lead to inaccurate and inefficient results of diminished value to management. It is not contended that the efficiency derived from incorporating the experience factor will more than offset the effort expanded in all possible cases, for only the criterion of relevancy can determine its efficacy. However, it is contended that the use of accounting results, where no attempt has been made to investigate the effects of experience, may be liable to serious error. In other words, if care is taken to introduce the factor of experience, and if the results obtained after such an attempt do not lead to increased efficiency, then its effects may be discounted. However, its implications should not be discounted on a priori assumptions, for not much effort might be needed to study the effects of experience in industrial situations. Definitions of Key Terms It might be advisable to attempt definitions for some of the terminology utilized, for it has to be admitted that the key terms used for the purpose of this study could lead to misunderstanding, if not properly understood. The reason is evident; the terms might have several accepted meanings, but might have been used in this study with special connotations.

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22 Experience and learning The word "experience" has been used to denote the phenomenon of gaining positive efficiency, observable in the form of quantitative improvement in the course of an operation being repeated over a period of time. In other words, while performing a repetitive operation, if improvement can be witnessed, the factors which aggregatively contribute to such improvement are collectively referred to as "experience." In the generally accepted sense of the terms (as witnessed by dictionary definitions), "learning" is contrasted to "experience" on the grounds that the former is knowledge acquired through study or instruction, as compared to "experience," which is defined as knowledge gained through actual performance of existential operations. This implies the dichotomy found in the study of philosophy as propagated by the rationalists and the empiricists, respectively. This distinction has not been accepted in the use of the terms. Rather, the term experience has been used to denote an interplay of existential and conceptual data which would be involved in the process of pursuing the desired goals. In this sense, learning may be considered synonymous to experience. However, there is a slight differentiation between the terms as used in this study. The term, "learning" has been used more in reference to the acquisition of knowledge on the part of an individual, as contrasted to the usage of the term "experience" which has been utilized to refer to groups or organizations. As the study is concerned more with firms and industries than with learning on the part of individuals, it

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23 has been deemed advisable to use the term "experience" to designate the phenomenon which leads to the quantitative improvement with the occurrence of repetitive operations in industrial situations. Reference to a repetitive event does not imply identical repetition, but merely one where there are points of similarity. Thus two operations might be substantially dissimilar; and yet, the initial might contribute some knowledge to a more efficient performance of the succeeding operation. To reiterate, the question regarding "why" human beings are susceptible to this phenomenon of experience is beyond the scope of the study. That this phenomenon can be observed, quantified, and used effectively for decision-making purposes is of prime importance for the research undertaken. Experience ciurve The function that results from plotting dynamic production data on any graph paper has been called an experience curve. Such a curve may be linear or non-linear, smooth or uneven, downward sloping, flat, or upward sloping. This explanation of the experience curve differs from the more generally accepted learning curve, which necessarily implies a downward op sloping smooth projection on logarithmic graph paper. However, it should be noted that there may be several types of experience curves; such as, the unit hour experience curve, the cumulative average experience curve, the lot average experience curve, and the cumulative total experience curve. Care should be taken to identify the

PAGE 34

24 type of experience curve involved, for each of the four stated above have different implications and uses. Experience factor, experience rate, and the slope of the experience curve The term experience factor is used to designate the existence of experience in a particular situation. Thus, the reference is more to the "factor of experience" or the "fact of experience," as vjitnessed in the situation being discussed. This can be contrasted to the experience rate, where a constant rate of improvement is involved. In this case, there is a specific quantitative rate which can be observed, and it is not just the general phemonenon of experience that is referred to. Whereas the experience rate is mentioned as a constant percentage decline in unit or cumulative average costs, labor hours, etc. for every doubled quantity, the slope of the experience curve denotes the exponential coefficient of the curve for use in mathematical calculations. Thus a 90 per cent cumulative average rate indicates that the cumulative costs or cumulative labor hours decline by 10 per cent with every doubled production. This 90 per cent rate may be represented on a downward sloping cumulative average curve, the slope of which can be expressed by the coefficient 0.152. Experience curve concept and experience curve technique The experience curve concept refers to the conceptual implications of the factor of experience on a generalized basis. In other words, the entire notion of experience and its implications for business in general are reflected upon.

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25 On the other hand, the experience curve technique refers to the specialized tool, commonly known as the "learning curve." Thus the technique requires the proper utilization of data to derive the experience rate, and its application for decision-making purposes. The utilization does not refer to any one specialized use but to its usage for aiding the solution of any problem toward which it can supply relevant data. If statistical or mathematical tools are employed for quantifying data, such that the experience factor is taken into consideration, then the experience curve technique has been employed. Managerial accounting tools, techniques, and concepts The three terms, tools, techniques, and concepts, aggregatively represent conceptual and practical aids utilized by the discipline of managerial accounting. In other words, it would be preferable to look upon the three terms as a set constituting any means used by the field for purposes of analyses rather than be reflected upon for their individual characteristics. Dynamic production data The term "dynamic" implies a continuity of operations for a given set of data. Hence the label "dynamic production data" refers to manufacturing information collected from continuous operations. This study is interested in the effect of change through repetition of production, therefore interest is centered on information which can separate the effect of acquired experience on production time and cost. The terms dynamic, cost-quantity, production time-quantity, volume, continuous,

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26 and repetitive production data or relationships have been used to refer to the same thing, namely quantitative information about production situations where considerable quantities are involved. Direct labor hours These hours refer to men-hours rather than the group or plant hours. Stated differently, a total of the hours worked by each individual on the job as opposed to the time spent by a group as a unit is referred to. For example, five workers assembling one unit in an eighthour day would be considered as utilizing a total of forty direct labor hours for the unit assembled, rather than the eight hours collectively worked on by the group. Linear projection and the linear hypothesis The linear projection refers to a smooth straight line on full logarithmic graph paper rather than on arithmetic grid graph paper or a semi-log graph paper, unless specifically stated. The linear hypothesis has been used by this study in reference to the "theory" that dynamic production data necessarily implies a constant rate of decline in costs and production hours with a duplication in the number of units produced. In other words, the linear hypothesis states that plotting dynamic data on logarithmic grid graph paper results in a linear projection. Research Methodology Employed Reasons for rejecting a case study approach It was the original intention of this study to undertake empirical case studies involving a range of situations. However, this mode of

PAGE 37

27 research was abandoned for several important reasons. In the first place, several studies can be found which relate to practical examples of specific situations and which lend support to certain hypotheses as formulated by the individual authors. Unfortunately, due to the constraints encountered in using a specific set of conditions as the basis for a study, there has been a tendency to state particular findings as generalizations. Most of the case studies indicate some form of applicability or the recognition of the experience factor to the particular situation, and hence are considerably limited in scope. This does not imply that the form of study is valueless; as a matter of opinion, it has great value. However, an undertaking of a detailed empirical investigation would have seriously limited the scope and value of the present study, for the author firmly believes that in order to conduct a reliable investigation, especially where internal financial information-gathering is concerned, one has to be an integral part of the researched unit, and the serious limitations encountered by an outside investigator might significantly impair the efficacy of the results obtained. This can be witnessed from considering the difficulties encountered by the author in his attempts at securing appropriate information. A great deal of time and trouble was expended in trying to get data on the American shipbuilding industry. An initial investigation had revealed that data from that industry could be particularly amenable for research purposes, especially since there were various sizes of shipyards which could be investigated. Unfortunately, a definite reluctance on the part of the industry to furnish data for the research led to the abandonment of all

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28 aspirations for an impirical investigation. Other attempts in this direction were also made but had to be similarly abandoned. The paucity of literature on the subject A rather dliitinct pocularity encountered in the courcc o£ the research was an apparent lack of relevant literature on the subject. The Accountant's Index to Periodicals referred to approximately twenty references over a period of almost half a century. The lack of literature was not quantitative in nature as it was qualitative, for a majority of the references were simplified recapitulations of the learning curve theory and its applications. Considerable effort was expended to secure and review all available literature, and if any work was overlooked it was either because of its unavailability, or that its existence was unascertainable despite all possible efforts. It may be asserted that the bibliography prepared by the study is perhaps the most comprehensive available on the subject. The approach used ^ Under the above-stated conditions, it was decided to rely, to a considerable degree, on the researcher's oxm experience and knowledge of the subject gained over a period of years. This knowledge, along with the available literature (including the case studies), has been utilized to investigate the subject. The emphasis has been on experimentation at the conceptual level, using existential data wherever appropriate. By "experimentation at the conceptual level" is meant the study of the implications using hypothetical data which could be adjusted to observe

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29 variations and effects on different situations. Wherever data from actual situations were available, such data were used in place of the hypothetical examples. In the derivation of the experience factor, statistical and mathematical means have been utilized, but not without proper care to understand their implications and limitations. The acceptance or rejection of otherwise non-substantiated assertions has been accomplished using the author's own experience and knowledge as the criterion. The remainder of the study has been conducted using conventional management accounting tools, techniques, and concepts, and introducing the element of experience to see the effect on the problem at hand. Thus, regular situations have been taken, the element of experience introduced into the situation, and the resultant conditions observed, x^7ith the degree of variations being noted. Solutions to the problems created by the added factor have also been sought and tested, wherever feasible. It is honestly believed that the advantages obtained by the use of hypothetical figures through a greater degree of maleability have more than offset the disadvantages encountered from not using actual data for validating hypotheses. Organization of the Remainder of This Study Since the subject matter of this study has been given consideration by various individuals and firms, it has been deemed necessary to undertake a historical review of the work done in the area. Such a task has been undertaken in Chapter II. Only a few important contributions

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30 have been briefly discussed, for other studies have done adequate tasks on historical reconstructions which can be referred to for further detail. The development of dynamic cost data for management usage has also been traced as part of the historical review. After distinguishing between "learning curves" as used for different purposes, a detailed critique of the business "experience curve" has been undertaken to point out its assumptions, characteristics, and general implications. Having pointed out the implications of the experience curve "theories," the role of the accountant as the person responsible for the collection of data which can be used for aiding management decisions has been probed. The task of recording, accumulating, and classifying production data which can aid quantification of the experience factor requires special emphasis and procedures which might differ from conventional methods. These differences are analyzed and enumerated. Furthermore, an important function performed by the accountant, namely interpretation of the data gathered, needs special emphasis and under standing, much more than a casual knowledge of the learning curve "theory" can supply. This task of interpretation can be efficiently undertaken only if one is aware of the various patterns and trends continuous production data can take. To give an idea regarding possible trends, a major portion of Chapter III has been devoted to explaining and illustrating different patterns observed in actual situations or under experimental conditions. Variations on the study of dynamic production data have also been explained in this chapter . That statistical and mathematical tools are involved in the study

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31 of dynamic relationships is a point hardly ever mentioned in accounting literature. In order for the analysis to be properly executed, some knowledge of the implications of these quantification tools would be necessary. For example, logarithmic graph paper can be used in place of plain arithmetic graph paper for plotting trends, provided the set of data can be expressed by the mathematical formula Y = ax . If this formula does not provide the best fit, the arithmetic grid graph paper might prove more beneficial. The point is that an unconditional usage of the logarithmic graph, as proposed by literature, may prove less efficient under certain conditions. Hence, statistical and mathem.atical implications have to be recognized, and Chapter IV has undertaken the charge of expressing their involvement. To aid analysis, a set of data collected in an actual manufacturing situation has been used, not to substantiate any generalized hypothesis, but merely for convenient illustration. A differentiation between the experience rate and the slope of the experience curve has also been attempted in that chapter. The mathematical quantifications demonstrated have been deemed important as aids for analyzing trends and qualitative judgm.ents to be used in decision making. The significance of the experience rate for interpretation purposes has then been analyzed, leading to a rather important consideration of the factors that affect the experience rate. Although an interdisciplinary approach would be necessary for proper research into the factors that contribute to the rate of improvement, an attempt has been made to enumerate pre-production and during-production factors. It is hoped

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32 that a framework for future research has been indicated for investigation of the factors that contribute to a decline in manufacturing time with increased quantities produced. Implications of the experience factor for specific tools, techniques, procedures, etc. have been investigated in Chapter V, where an arbitrary classification has been used for purposes of analysis. Thus, particular effects for costing of materials, labor, manufacturing overhead, distribution expenses, and administrative expenses, for ascertaining unit costs and profits, for evaluating and forecasting inventories, and implications for the division of costs into their fixed and variable element have been analyzed under the section on costing. Forecasting labor requirements, setting wage incentive schemes, budgeting, pricing, and selecting between alternatives, such as make-or-buy, constitute some of the more important subjects investigated under the section devoted to planning implications. Cost control, how it is affected by the factor of experience, and how this factor could be incorporated for better analysis have been viewed in the section on control implications, where control charts, standard costing procedures, design change measurements, and other less celebrated control aids have been selected for discussion. The final chapter has been devoted to an enumeration of the conclusions reached in the course of the study. It also contains a note on the possible avenues for future research in the area, research that could conceivably prove fruitful.

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33 Cliapter I 1. For definitions of some terms used in this report see pp. 21-26. 2. R. M. Barnes, J. S. Perkins, and J. M. Juran, "A Study of the Effects of Practice on the Elements of a Factory Operation," University of Iowa Studies in Engineering , Bulletin 22 (November, 1940), pp. 3-86. 3. W. Z. Hirsch, "Manufacturing Progress Functions," The Review o f Economics and Statistics , XXXIV (May, 1952), 143-155. 4. W. Z. Hirsch, "Progress Functions of Machine Tool Manufacturing," Econometrica , XX (January, 1952), 139. 5. A. D. Searle, "Productivity Changes in Selected Wartime Shipbuilding Programs," Monthly Labor Review , LXI (December, 1945), 1132-1147. 6. K. A. Middleton, "Wartime Productivity Changes in the Airframe Industry," Monthly Labor Review , LXI (August, 1945), 215-225. 7. W. B. Hirschmann, "Profit from the Learning Curve," Harvard Business Review , XLII (January-February, 1964), 125-139. 8. National Aeronautics and Space Administration, Guidelines for Evaluation of Contractor Accounting Systems , NHB 9090.6 (February, 1967 Edition), Para. 905. 9. National Aeronautics and Space Administration, Procedures for Reporting Cost Information from Contractors , NHB 9501.2 (March, 1967 Edition), pp. 57-58. 10. For example. Alpha and Omega and the Experience Curve , Directorate of Procurement and Production, U. S. Army Missile Command, Redstone Arsenal, Alabama (April 12, 1965). Also, "Improvement Curve Analysis Techniques," Defense Contract Audit Manual , Appendix F (July, 1965). 11. A. W. Levi, Varieties of Experience (New York: The Ronald Press Company, 1957), p. 3. 12. Some philosophical views on experience have been discussed in Levi's work. For a unique approach, H, T. Deinzer's Development of Account ing Thought (New York: Holt, Rinehart and Winston, Inc., 1965), Chapter IV, can serve as an excellent reference. 13. J. A. McGeoch and A. L. Irion, The Psychology of Human Learning (New York: David McKay Company, Inc., 1961), p. 2.

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34 lU. E. R. Hilgard and G. H. Bower, Theories of Learning (3rd ed. New York: Appleton-Century-Crofts, 1966), pp. 1-2. 15. Ibid. 16. R. Bellows, "The Management of Learning: Theory and Practice," Personnel Administration , XXIII (January-February, 1960), 22-28. 17. H. Asher, Cost-Quantity Relationships in the Airframe Industry , Project RAND R-291 (California: The RAND Corporation, July 1, 1956), p. 191. 18. T. P. Wright, "Factors Affecting the Cost of Airplanes," Journal of Aeronautical Sciences , III (February, 1936), 122-128. 19. A. B.Berghell, Production Engineering in the Aircraft Industry (New York: McGraw-Hill Book Company, Inc., 1944), Chapter XII. 20. K. F. Hammer, "An Analytical Study of 'Learning Curves' as a Means of Relating Labor Requirements to Production Quantities" (unpublished master's thesis, Cornell University, 1954). 21. Asher, op. cit ., p. 9. 22. Hirsch, Review of Economics and Statistics , p. 143. 23. The one reference mentioned was Paul A. Samuelson, Economics : An Introductory Analysis (New York: McGrav7-Hill Book Company, Inc., 1948), pp. 473-474. 24. A. A. Alchian, "Costs and Output," The Allocation of Economic Resources , M. Abramovitz _et al. (California: Stanford University Press, 1959), pp. 23-40. 25. J. Hirshleifer, "The Firm's Cost Function: A Successful Reconstruction," The Journal of Business , XXXV (July, 1962), 235-255. 26. "The Field of Management Accounting," N. A. A. Bulletin , XLIV, Section III (June, 1963), 7. 27. Several textbooks can be referred to for a detailed treatment of the nature and scope of managerial accounting. To suggest one: C. L. Moore and R. K. Jaedicke, Managerial Accounting (2nd ed., Dallas: Southwestern Publishing Co., 1967). 28. For further details, refer to Chapter II,

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CHAPTER II EXPRESSING THE DYNAKEC RELATIONSHIP BETWEEN COST OR PRODUCTION TIME AND THE QUANTITY PRODUCED Purpose and Organization of the Chapter Before an investigation can be undertaken to study the derivation and understand the implications of the experience factor for managerial accounting, it is necessary to review and consider what has already been done in this direction. That a relationship exists between production time or cost and cumulative production is by no means a contribution of this study, for a considerable amount of work has been done to support this contention. Unfortunately, literature available on the subject, though abundant, often appears to be over-simplified, vague, and even contradictory, mainly due to the fact that most authors prefer to follow the accepted "pattern," and rely on "theories" based on implied assumptions without a proper understanding of their implications. Most of the information on the production time-quantity relationship is available under the subject-title "learning curve," or "progress curve," and although the subject of this research is closely connected to the "learning curve," there is a significant difference which will be noted in the course of this study. The main intention of this chapter is to investigate the "learning curve" theory as an explanation of the dynamic production time-quantity or cost-quantity relationships as observed in industrial situations. Does the "theory," as proposed and accepted by so many authors and practitioners, really serve as a reliable representation for ordering exis35

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36 tential and conceptual data to aid business management in its function of decision-making? An answer to this question has been the principal aim of the chapter. In order to obtain an acceptable answer, it has been deemed necessary to trace a short historical sketch of the "learning curve" concept, observe its acceptance and applicability, and define its characteristics. The different "theories" and their implied assumptions as "accepted" over the years have been explained and critically evaluated in the course of the chapter, keeping the managerial accountant's point of view in mind. Particular emphasis has been placed on analyzing the "linearity assumption" as a means of expressing production time-quantity relationships, since most of the accounting literature seems to imply a universal applicability for this form of representation. This investigation is supposed to pave the way for Chapter III, where more detailed analysis of possible production time-quantity relationships which could be profitably utilized by the managerial accountant have been indicated. A Historical Sketch of Contributions to the Establishment of a Cost-Quantity Relationship PreWorld War II experience It was in the airframe industry that peculiarities and trends in production time-quantity relationships were initially observed. ^Miguel A. Reguero has asserted that the credit for original investigation of airframe production data should be bestowed upon Leslie McDill, Commanding Officer at McCook Field (predecessor of Wright-Patterson Air Force Base,

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37 both near Dayton, Ohio). Reguero's research indicated that it was McDill's efforts in 1925 which led to the formulation of the "learning ,,2 curve theory. However, Dr. T. P. Wright has generally been looked upon as the pioneer who researched into the implications of continuous production. T. P. Wright, while still a manager of the Buffalo plant of CurtissWright, presented a paper for the Aircraft Operations Session at the Fourth Annual Meeting of the Institute of Aeronautical Sciences, which was later printed in the Journal of Aeronautical Sciences , February, 1936, under the title "Factors Affecting the Cost of Airplanes." In this paper Wright pointed out that he became interested in the effects of quantity production on cost around 1922, and the results of his empirical investigations have been graphically presented in the above-mentioned article. This publication was the first attempt at a graphical representation of production data on logarithmic graph paper, and the first attempt at defining the linear dynamic cost function. Wright observed that as cumulative production increased, the average cost per unit of the product in question decreased. Not only did it decrease, but this decline followed a particular pattern. It was noted that the average labor and material cost per unit declined by a constant percentage with every doubled quantity produced. Thus, when plotted on logarithmic graph paper the curve that resulted was a negatively sloped linear function. This, then, was the first mention of what was later referred to as the "learning curve." An interesting point in Wright's article is his classification of cost into the three elements of labor, material, and

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38 overhead, for purposes of analysis. Most students of the subject would partially concur with S. A. Billion, who observed that "although it is now a widely acknowledged fact that labor and overhead vary as the quantity of units produced is increased, there has been a surprising lack of 5 development on the direct material curve which Wright has suggested." There does not appear to be any other important work on the implications of quantity on cost or production time between 1936 and the beginning of World War II, and perhaps the next publication may be the nondated study by J. R. Crawford for Lockheed Aircraft Corporation. During and after World War II Since 1940, several individuals connected with varied disciplines, corporate bodies, and research institutions have contributed to the study of production time-quantity or cost-quantity relationships. Although the temptation to undertake a detailed evaluation and review of the historical significance of the different contributions is very strong, such an endeavor has been by-passed, for other capable treatments of the subject are available. For example, Harold Asher's Cost-Quantity Relationships in the Airframe Industry provides an excellent treatment of the historical reconstruction and evaluation of literature on the subject, from Wright's first article to 1955, around which time Asher's work was published. In order to avoid duplication, a mere mention is made of the important contributors and their contributions. Only publications which have not previously been commented on, and which have been considered significant for this study, have been reported.

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39 The work of J. R. Crawford of Lockheed Aircraft Corporation needs special mention." Crawford \ms one of the most respected authorities on the subject, and as such was called upon to conduct special studies by the Stanford Research Institute and the Air Material Command of the United States Air Force. Working along with Edwin Strauss, the now-famous Crawford-Strauss Study was published for the Air Material Command in 9 1947.The contributions of P. B. Crouse, -^^ A. B. Berghell, K. A. Middleton, ^ G. W. Carr,"*-"^ G. M. Giannini, "'^ P. Guibert,-""^ E. Mensf orth, "^^ W. Z. Hirsch, F. S. Hoffman, and Armen Alchian have been commented 20 on at length by Harold Asher. The only notable work missing in this list of earlier contributions is that of A.D. Searle, who made a study of the U. S. shipbuilding industry for the Monthly Labor Reviex>7 in a manner similar to that of K. A. Middleton, whose study had been conducted on the airframe industry. ^^ The works of Miguel Reguero^^ and Harold Asher have been commented on, and evaluated, by R. P. Zieke in his unpublished thesis, submitted to Stanford University. The Harvard Business Review published an article by Frank J. Andress which, in the opinion of this writer, is an excellent introductory article on the subject, in which the "theory" of the learning curve has been explained, limitations pointed out, steps for application enumerated, and mention made of different industries that could profitably use the learning curve. ^^ A decade later, another noteworthy article was published in the Harvard Business Review , by Winfred B. Hirschmann, in which the long-run effects of experience were pointed out

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40 and substantiated by empirical evidence. Hirschmann's thesis appears to be that improvement can continue indefinitely, and can be actually produced, or enhanced, by a concerted effort on the part of higher management. The field of industrial engineering has produced considerable work toward the study of production-time-quantity relationships. A notable contribution from this area has been the work of R. W. Conway and A. 27 Schultz. Along with the various observations made in their exhaustive article are published the results of a study conducted using four firms which had not used dynamic production data for control purposes. It was found that although cost declines were evident, there appeared to be a leveling off in a few cases where production had reached large quantities. The results of an empirical study involving three hundred Southern California metal product manufacturers have been presented by Reno R. 28 Cole. According to this study, 61 per cent of the respondents stated that they used learning curves, although most suggested caution in its usage. An article by E.B. Cochran, which has hardly ever received mention, 29 is nevertheless worthy of comment. Cochran has asserted that the learning curve technique has been dying in popularity due to certain inherent weaknesses. He made a careful examination of the basic cost function, and attempted to develop new concepts, including the suggestion for a "unit of learning." It has been implied that the linearity assumption (as will be discussed later in this chapter) can be misleading, and the proper functional representation may be the S-shaped curve, referred to earlier by G. W. Carr.-^°

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41 A much heralded, but a rather disappointing study was undertaken under the aegis of the Institute of Business and Economic Research at the 31 University of California by E. C. Keachie. With the help of a questionnaire and a guided empirical study, Kcachic attempted to substantiate the thesis that production time-quantity relationships are as important to small business management as to the larger firms, irrespective of the industry with which they are connected. Reference to the implications of dynamic production data has also been made in accounting literature by a few writers. Mention must be made of Rolfe Wyer, Ronald Brenneck, R. B. Jordan, Sanders and Bly35 36 37 stone, -^ V. J. Shroad, and Arnett E. Burrow, among the various accountants who have referred to the factor of experience as an important element which should be taken into consideration for accounting analyses. Contributions made by corporate bodies and research institutions cannot be bypassed in a historical reconstruction of this nature. Almost all of the major aircraft corporations have issued manuals and studies — one of these mentioned earlier regarding J. R. Crawford's work for Lock38 heed Aircraft Corporation. Special mention may be made of Tommie Fowlke's manual for Convair Corporation, which was recently re-issued by 39 General Dynamics, Fort Worth. The distinct approach and the care for detail illustrated by Fowlkes was of considerable interest to the present study. A considerable amount of research has been accomplished at two 40 research institutions: The Rand Corporation, and the Stanford Research 41 Institute. Most of the studies were financed by the Air Material Com-

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42 mand of the United States Air Force, and no student of the subject at hand could conduct a study without indicating his appreciation to the Armed Services of the United States of America for their role in the development of knowledge in this field. Development of the Linear Logarithmic Dynamic Cost Function T. P. Wright's "Eighty Per Cent Curve" The implications of quantity produced on the production time and cost of the product were first noticed in airframe production, as pointed out earlier, and the relationship was initially referred to as the "eighty per cent curve." To quote T. P. Wright, "This 'eighty per cent' has a definite meaning in that it represents the factor by which the average labor cost in any quantity shall be multiplied in order to determine the average labor cost for a quantity of twice that number of airplanes." In other words, the average labor cost per unit of product indicated a 20 per cent decrease between doubled quantities. Thus, if the cumulative average labor cost for the production of ten units happened to be $10,000 and if ten more units were produced, the cumulative average for all the twenty units would be $8,000 per unit; that is, a 20 per cent decline in average labor cost with an equivalent production in units. This "eighty per cent curve" came to be generally accepted, especially by the Pacific coast airframe manufacturers, although used by some 44 under a different interpretation. For example, J. R. Crawford of Lockheed Aircraft Corporation agreed with the linear relationship, but he felt that such a relationship existed between the quantity produced and the individual 45 unit man-hours, as opposed to the cumulative average. Another variation

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43 was where lot-averages were plotted against unit costs or labor hours to 46 arrive at linear functions for the "eighty per cent curve." It was not long before the hazards of generalization were noticed and separate functions were derived by each company to suit its peculiar production process and product. The generality of the "eighty per cent curve" has been indirectly refuted over the years in various x^ays by students of the dynamic relationship. An early study which directly challenged the validity of an industry-wide "eighty per cent curve" was undertaken by A. Alchian who asserted that the available statistical evidence was overwhelming against its general application. He concluded that: Extensive analysis by the Economics Division of the RAND Corporation indicates beyond all doubt that the slopes are different and that the heights are different among the plants producing airframes. Even between two manufacturing facilities producing the same type of airframe the heights and slopes are different.^' This assertion was restated by Alchian in another Rand study pubA Q lished a few months later. In this later study, Alchian used statistical analyses involving predicted and actual values to determine the reliability of different types of average curves. The data seemed to indicate that absolute differences between predicted and actual values (properly weighted by actual man-hours) averaged 25 per cent of the actual, where predictions were based on an industry-wide average curve, and also where 49 predictions were based on a general airframe-type progress curve. This analysis cast considerable doubt on the acceptance of "generalaverage" type projections, and indicated the necessity for further research into each specific situation.

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44 During and after World War II Since the beginning of World War II, interest in the production time-quantity relationship has spread to areas other than the airframe industry, and reference has usually been to the "learning curve" or the "manufacturing progress curve" concept and technique. This learning curve refers to the resultant function of production data plotted on logarithmic graph paper, indicating a constant percentage decline in costs or labor hours between doubled quantities. This is the same as the "eighty per cent curve" referred to earlier, except that the learning curve slope could represent any mathematical quantity between a feasible range and not just one point within this range. Although this concept of cost-decrease due to improvement or experience or learning has come to be knoxm by m.any other names, it is still most popularly referred to as the "learning curve." Appendix A contains a list of various names used to describe the relationship between cost or labor hours and quantity of production. The last two decades have witnessed a slow but steady acceptance of the concept and technique by industries outside the airframe production type. A few industries where production time-quantity relationships have actually been utilized for decision making (as differentiated from where the relationship could be utilized) have been mentioned below. Reno R. Cole's study, referred to earlier, indicated that 61 per cent of the 300 Southern California metal product manufacturing industries, other than airframe, utilized the cost-quantity relationship. Included in this list of industries were precision mechanical electro-optical

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45 instruments, electronic unit manufactures, mechanical-hydraulic electrical unit manufacture, large built-up laminated plastic aircraft assemblies, and electronic data processing equipment manufacture. Application of labor cost-quantity analysis to a multi-product industry has been claimed by Paul F. Williams on the basis of data collected at United Control Corporation. In an unpublished paper presented on behalf of International Business Machines Corporation, Donald A. Schreiner has given examples of how productive time-quantity relationships have been utilized to aid opera52 tions at I. B. M., Endicott. The point that management is considerably aided has been strongly asserted. E. C. Keachie's recent study, mentioned earlier, has pointed out the benefits derived by small manufacturers who utilized the relationship. The usage of dynamic production data by small manufacturing firms was evidenced by this author while on a visit to a small walkie-talkie manufacturing plant employing around thirty people. It was surprising to find the accountant maintaining elaborate charts depicting production timequantity relationships, which he asserted were very helpful to him. W. B. Hirschmamin his study has shown its application to several industries such as petroleum, electric power, basic steel, and construction. Included in his group of examples are actual situations encountered including one involving DuPont's petrochemical works. John N. Siersema has indicated the application of the learning curve by a high frequency electronic tube manufacturing concern. An interesting point in his presentation is a description of the company which

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46 was studied, including details regarding the accounting systems and pro; fol lowed. -^^ In the course of private correspondence with the author of this study, Irving J. Sandler, Chief, Special Projects Division, Defense Contract Audit Agency, has presented an interesting list of industries and functions in connection with which the Agency has applied the experience curve methodology. Included in this list are the manufacture of electrical and electronic components for major weapon systems, manufacture of controls and instruments for a variety of propulsion system.s, m.unition applications, and missile production activities. Sandler is emphatic in his assertion that the "analytical technique is by no means confined to the airframe production industry." The Learning Curve The learning curve is a statistical or mathematical representation of production data which can be used to aid management in the functions of planning and control. It is based on the concept that as operation is repeated, there is opportunity for experience to generate improvement, which leads to lower production time or cost for subsequent units manufactured. Thus, as a task is duplicated, the learning derived through repetition gets embodied into lower costs or production time for later quantities produced. An hypothesis has been stated in the form of the learning curve "theory," to be used in business or manufacturing situations, based on this phenomenon of improvement. The phenomenon should be differentiated from the learning curve "theory," as the "theory" is supposed to provide

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47 a means for ordering data to aid management in the task of planning and control in actual industrial situations. The concept of "learning" has also been used to develop another type of projection referred to as the "learner curve" or sometimes as the "learning curve," which has been utilized for incentive wage payment schemes. The discipline of psychology has also been concerned x<7ith the phenomenon of learning and graphical projections, often referred to as "learning curves," which have been used for clinical analyses. To avoid any misconceptions regarding these "learning curves," a detailed distinction has been attempted below. A distinction between three "learning curves" It may be unfortunate that the dynamic production time-quantity relationship has come to be referred to as the "learning curve." There are two important reasons for the above contention. In the first place, the word "learning" implies a narrower applicability of the dynamic production time-quantity relationship than vjhat this relationship actually involves. The term "learning" often gives the impression that the concept is applicable only to the worker who is directly connected with production operations. In other v7ords, a false impression regarding the applicability of learning on the part of the direct laborer as the only criterion which leads to improvement x^ith increased production may be generated. The truth is that the "learning curve" concept as used by management is concerned with improvement gained in several different ways, of which the individual worker's learning can be considered only a contributing factor, as indicated in Chapter IV.

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48 A more important reason for considering the term "learning curve" as inappropriate lies in the fact that the same term has been used to refer to other more appropriate tools, concepts, and techniques. For example, psychologists have used "learning curves" to measure and analyze learning trends in individuals, and it is perhaps this usage which led to the term being borrowed for production data analyses. The term "learning curve" has also been used for a graphical representation to aid incentive payment schemes where experience at the job might be an important criterion for efficient production. Although all three "learning curves" deal with the phenomenon of learning, or experience, or improvement, each is used to serve distinct functions. The psychologist's learning curve deals mainly with learning patterns as observed in individuals, and has been used in psychological analyses to answer questions such as, how or why does learning take place in a particular individual under peculiar conditions? Also, what can be done to improve learning? In other x^7ords, the curve helps in analyzing learning as a mental process. An excellent reference on the use of learning curves in psychological analyses has been provided by McGeoch and Irion's The Psychology of Human Learning . The authors define a "learning curve" as a line of regression of performance upon practice, where practice is the kno\-m vari58 able and performance, as a result of practice, is the unknoxm. Figure II-l indicates representative forms of learning curves when trials or some other measure of practice are plotted on the X axis and the corresponding measures of performance on the Y axis. An example of an actual learning

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49 Practice 3l mss MiDaiaijittJ: FIGURE n-1 REPRESENTATIVE "LEARNING CURVES" AS USED FOR PSYCHOLOGICAL ANALYSES t

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50 curve of one practiced subject for learning a list of words has been illustrated in Figure II-2. McGeoch and Irion state, "there is no single curve of learning which can be called the curve of learning. Different tasks, experimental procedures, methods of measurement, and types of subject will yield different forms of learning curves." Tlie point to be noted is that these learning curves are derived by observing individuals at particular tasks under experimental conditions. The graphical representation used for purposes of providing wage incentives has often been referred to, more appropriately, as the "learner curve." An example of a learner curve has been illustrated by L. A. Barron, who has used a descending step-like formation to indicate a m.eans for compensating new workers during the learning period."^ Frank J. Powers has provided a graphical representation which he has referred to as the "learning curve" to help develop realistic incentives for workers on short-run jobs. Figure II-3 is an example of such a learning curve on arithmetic grid paper. The use of logarithmic graph paper to determine incentive learning curves was initially explained by J. R. Hadley, who illustrated his learning curve as an upward sloping linear function. Logarithmic paper has also been used by Lou Wertman, whose learning curves for individual workers are very much like the projections used for business decision-making. It has been noted that although these "learning curves" incorporate the same phenomenon used to describe production cost-quantity relationships, there is a difference of purpose and a variation in means employed in the process of calculation. Although these two learning curves may be considered

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62

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53 as elements of the same species, there are significant differences, therefore distinct references may be advisable. In the opinion of this author, the term "learning curve" is best suited for the psychologist's graphical representation, and is certainly less descriptive of the phenomenon considered under the production timequantity relationship used for business decision-making. The graphical representation used for wage incentive schemes may be appropriately referred to as the learner curve to signify its applicability to incentive schemes . The terms "experience curve," "progress function," "improvement curve," or "time-reduction function" appear to be more descriptive of the phenomenon involved in the production time-quantity relationship as utilized for business planning and control, than the more accepted title 64 "learning curve." For the remainder of this report, the "learning curve" used for business decision-making will be referred to as the "experience curve," to differentiate it from the other two namesakes. Alternative means of projecting data The importance of the experience curve has been based on the understanding of a basic mathematical concept — the logarithmic scale. Almost all explanations available on the subject utilize the logarithmic scale in preference to the arithmetic scale, and the value of the experience curve as a tool for planning and control has been made dependent on the successful use of logarithmic scales. The reasons for this approach are explained below. A graphical representation of continuous production data can be

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54 obtained by plotting costs or labor hours per unit against the number of units produced. Consider the hypothetical production data presented in Table II-l. A mere glance at the table indicates that the labor hours per unit have been declining with increased production. This information when plotted on arithmetic grid graph paper appears in the form of a hyperbolic function, indicating a fast initial decline which straightens out and turns asympototic to the X axis, as seen in Figure II-4. The reason for this functional form is that plain arithmetic grid graph paper represents equal amounts of differences by equal distances (denoted by the spaces) in terms of absolute figures. Thus a change from one to two units represents an absolute difference of one unit, just as the change from five to six, or one-thousand to one-thousand-and one unit represents an increment of one unit. Although the absolute differences are the sam.e in all these cases, the relative differences are unequal. For example, the increase from one to two units represents a 100 per cent increase, from five to six is a 20 per cent increase, whereas from a thousand to a thousand and one units represents an increase of only .01 per cent. It is usually argued that if one's intention is to visualize a relationship between two variables in the initial stages of production, then the nonlinear graph might prove advantageous. In other words, for a "quick" look at the effect of experience on initial units produced, this function might serve the purpose. However, if it were necessary to obtain data through extrapolation (or even interpolation), especially for extremely large quantities, this curve might prove inefficient and cumbersome. For example, to plot data for five thousand units, the graph would have to be

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TABLE I II Selected Values from an Hypothetical Cumulative Production Schedule Unit Number

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S€ is —J ^ "* < ul LU — _ oe Of 3 u. < O O ^ Z < »Ui «/) Ui Of o. UJ < X < O ^ o 3 •O E u Labor Hours Per Unit

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57 extended 125 times horizontally, and the projection for the last fortyunits would then be as in Figure II-5. The absurd length of the graph, plus the limited value of the projection at high production levels restricted utility for this mode of presentation. However, this argument has not been found acceptable by this study for reasons explained in Chapter IV. Some of these shortcomings of the arithmetic grid graph paper can be avoided, it is asserted, by plotting the data on logarithmic grid graph paper. Thus, if the data presented in Table I were plotted on logarithmic graph paper, the result obtained would be a negatively sloped linear function as shown in Figure II-5, which would be expressed mathematically as the linear exponential function: Y = A X~ (indicating a constant rate of decline) . In other words, if the intention is to measure relative rates of change, rather than absolute amounts, without being influenced by the size of numbers, then the data have to be plotted on logarithmic graph paper which can indicate relative relationships. Just as the distance between units two and four would be the same as the distance between units ten and twelve on arithmetic grid paper, that is, the absolute differences being represented by two units in both cases; logarithmic graph paper is so constructed that equal distances represent equal percentage changes. Thus, the distance between two and four units, which represents 100 per cent change, would be equal to the distance between units three and six, or units five and ten, or units seventy and 140, etc., each of which represents 100 per cent change. The logarithmic graph paper referred to is the full logarithmic paper, or one xvith both axis marked in logarithmic scales.

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UJ « > Ui UJ < U < Q Z M S I Ui J tt ^ z 3 « O O < ;i -Z^ O Q O < O 2 > 3 o o a.

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59 as already seen in Figure II-6 which is different from semilogarithmic 67 paper which has one logarithmic scale and another arithmetic scale. Full logarithmic graph paper is constructed so that distances between numbers on cither scale represent equal percentage changes. Tliis full logarithmic graph paper is also referred to as double-log, full-log, log-log, rate, 6 Q slide-rule, and ratio-graph paper. The following list is an adaptation of observations made by Kroeker and Peterson who have pointed out several characteristics of logarithmic graph paper. a. A straight line on logarithmic paper means that the rate of change between txco variables is a constant. b. There are no zeros — values approach zero, but never achieve it. c. The graph paper is dra^m in terms of cycles such that the first cycle starts with one and ends \
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60

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61 line for planning and control purposes more efficiently utilized. It may be reiterated that the trend line need not be linear, for as long as a pictorial quantification of production data can be indicated, such a representation can be utilized as explained later. It would be pertinent to point out that although the advantages of logarithmic scale utilization have been well appreciated by this study, the overemphasis on this mode of analysis has also been noted. Further discussion of the subject has been undertaken in Chapter IV, where the findings of this study, as contrasted to accepted procedures just pointed out, have been discussed in detail. Characteristics of the experience curve I. Since the cost per unit varies inversely with the quantity produced, the function would be negatively sloped. An upward sloping curve is possible, but would signify deterioration or inefficiencies through gaining experience, which would be unusual but possible. II. The function is a dynamic cost function, and not a static cost function, as it is the cumulative production which is one of the variables, and not "rate" of production. This point was discussed earlier in Chapter I. III. Technology is not assumed to be constant. As a matter of fact, it is the changing technology x\rhich is depicted by the lower costs. A distinction is made here between technology changes and changes in the techniques of production as pointed out by A.Alchian. Technology is taken here to refer to the state of knowledge, whereas techniques of production refer to fixed assets such as land, equipment, and production

PAGE 72

62 processes. In other words, a change in technology refers to improvement on the part of the workers, supervision, management, better engineering design, more efficient tooling, sm.oother coordination betx>7een functions, along with other factors mentioned in Chapter IV. Techniques of production are taken here to refer to what is commonly considered in accounting terminology as "capacity to produce." If the relationship analyzed is for a product, changes in the techniques of production might necessitate a new curve, and hence they are assumed to be constant. On the other hand, changes in the techniques of production, when quantified, might indicate the efficiency derived through experience, if curves are plotted for entities or industries, in which case even the techniques of production may be considered variable. However, where individual products are concerned, production capacity is assumed to be constant, whereas technology is considered variable. rv. Yet another characteristic is that the data signify continuous production. In other words, if production on this product or process is discontinued for a substantial period of time, such that the experience gained m.ay be adversely affected, then the shape of the learning curve would also be affected. Therefore, in order to arrive at a linear function, continuous production has to be assumed. V. There is an assumption of homogeneity of product or process for which the learning curve has been plotted. Minor design changes would be incorporated into the same curve. However, substantial changes would necessitate a new function. VI. There has to be consistency in the type and mode of data collection, such that differences in data do not affect analysis.

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63 VII. The percentage attached to the learning curve indicates the rate of improvement. This rate implies a constant percentage of decrease ^Tith doubled quantities, and is expressed by the complement of this rate of decrease. Thus, as discussed earlier, the 80 per cent slope indicates that the decrease in costs between doubled quantities would be 20 per cent at all levels of production . In other words, once the learning curve slope has been established, the percentage decrease would be the same for, say, increase in production from one to two units, or twenty to forty units, or 300 to 600 units, or even from 1,000,000 to 2,000,000 units. This is mathematically expressed by the linear function Y = AX"-^. It is this characteristic that initially created an interest in the experience curve. The simplicity of the straight line with which one could utilize production data for more accurate forecasting, which was implied by the linear characteristic, was responsible to a considerable degree for the early acceptance of the experience curve; and by the same token, it is this simplicity which might be responsible for its stunted growth. VIII. The reference to a "linear" logarithmic function does not imply that production data have to fall exactly on the smooth path. When plotting actual data the chances of finding a smooth straight line are almost phenomenal. However, a smooth projection may be derived by using statistical tools, such as the line of best fit using least-square computations. In other words, a relative decline may be evidenced by observing the plot points through which the line of best fit can be dra^-m. Such a line may be drawn for the cumulative average or individual units hours or average unit hours, depending on the observer's judgment regarding

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64 linearity. More on this subject of statistical implication will be discussed in Chapter IV. A Critique of the Conceptual Implications of Experience Curve "Theories" What is the "theory" behind the experience curve? As initially stated by Wright, the answer might be phrased as something to this effect: as production is doubled, the average labor cost per unit declines by a constant percentage, between the doubled quantities. That is, if cumulative average cost per unit were to be plotted against the cumulative number of units produced, the result would be a linear function on logarithmic graph paper. Howe\'er, the airframe manufacturers and users of the experience concept in a few other industries found that the above statement could be refuted on grounds of empirical data collected which indicated that the cumulative average when plotted on logarithmic graph paper was not a straight line, at least not in the initial stages of production. Several users contended that it was the unit hours as plotted against cumulative production that resulted in a linear function, and the cumulative average function was 73 curvilinear in the initial stages of production. Yet another interpretation, one which was (and still is) widely accepted, requires plotting averages for specific lots against cum.ulative production and arriving at a linear cost function X'Jhich is referred to as the lot average learning curve. Beyond the initial production, it is usually agreed by proponents of the experience curve theory that the curve will follow a linear trend.

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65 In other words, once the curve has settled dovm, one would find a fairly straight projection from further production provided there are no substantial changes. What the theory involves is interesting to note. It implies that once a few values for units produced are secured, this limited information can be used by managem.ent in decisions regarding planning and control of operations, for the theory states that a definite pattern of constant per centage cost decreases for doubled quantities mil ensue . The universality of acceptance awarded this proposition is overwhelming despite several studies made which seem to point out the possibilities of other form.s of the production time-quantity functions. It is acknowledged that several studies have been conducted which seem to indicate a high degree of correlation for the linear representation; however, the point to be noted is that there are as many empirical observations which have indicated nonlinear trends. In other words, there is empirical evidence to support any of the contentions above, that either the cumulative average curve or the unit hours curve or the lot average curve can be plotted to arrive at a linear function on logarithmic graph paper. However, there are other findings which indirectly challenge the contention of linearity. For example, Gardner Carr formulated what he called an S-shaped curve. '^ Wright had pointed out the possibility of a gradual levelling-off curve. This pattern was also observed by Conway and Schultz, among others. The Stanford Research Institute insisted on the recognition of a humped curve to represent initial 78 production. Discussion on these and other different patterns has been

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66 avoided at this point, for a major portion of the next chapter has been devoted to the different patterns observed in production time-quantity or cost-quantity relationships. The .point is that if the linear representation can be proved to be conceptually sound as well as empirically verifiable, then a universal proposition can be stated in the form of a "theory." However, if contrary assertions can be made, the proposition cannot be stated in the form of a "theory," but may be presented as a possible explanation for a particular set of conditions, or can be used as an approximation for purposes of analyses simplification. The remainder of this chapter represents an investigation of the conceptual inconsistencies involved in the acceptance of a linear projection, whereas the next chapter contains an investigation into some emprical findings. It is acknowledged in the field of cost accounting that the total cost of a product is composed of several elements which can be recognized as having been incurred for the production of the product. As regards manufacturing or production cost, segmentation of portions applicable to direct material, direct labor, and manufacturing overhead is undertaken 79 to facilitate managements planning and control functions. Assuming that the total cost of a hypothetical Product X can be classified into these three segments, the effect of increased production can be analyzed by experimenting with the data presented in Table II-II. It will be noticed that the material cost per unit is declining at a much slower rate than the decline noticeable in the per-unit labor and overhead costs. If the data presented in Table II-II were plotted on logarithmic paper, the individual learning curves for material, labor.

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TABLE II -II Selected Cost Data for Product X 67

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68 overhead, and the total cost curve would be as shovm in Figure II-7. We can observe that although the curves for the cost segments are declining at a constant rate, the total cost curve which is a summation of the individual segments is not a linear function, but is convex to the point of origin. The reason for this curvilinearity is obvious. The total cost curve is a mere summation of the individual elem.ents; hence, it will first be pulled down by the cost element which has a steeper slope, but after a certain point, its rate of decline will be lessened by the slower decline-rate cost elem.ent, in this case, material cost. The point that emerges is that if improvement takes place at the same rate for all elements of cost, then the total cost line would be linear on logarithmic paper. However, as will be seen, the opportunities for improvements are more abundant where time taken for production is involved than for cost of m.aterial content. The assumption that all elements contributing to total cost have the same rates of decline may not be valid, and if this is so, the linearity assumption for the "learning curve" would have doubtful validity. How valid is the linear representation for the different elements of cost? How much more reliable wDuld projections be if costs were broken down into different elements and their relationships with quantity produced observed? Perhaps more acceptable than the total cost-quantity relationship, but, then, these elements of costs are individually made up of sub-elements. Thus the labor cost would include costs incurred on different operations, which might be susceptible to different rates of improvement, as indicated below. The labor hours expanded on a particular unit may be m.ade up of several different types of operations. For exam.ple, Asher has illustrated

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69 /

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70 the effect of different improvement rates for major and final assembly, sub-assembly, and fabrication, on the unit curve which turns out to be considerably convex, as can be seen in Figure II-8, which has been adapted from Asher's presentation. Yet another consideration may be the number of times an operation is performed during the course of producing one unit. For example, while assembling a special truck body, four gadgets of the same type might have to be assembled and mounted. The opportunity for gaining experience in mounting this gadget would be much more than another widget which has to be mounted only once per truck. In other words, there could be different rates of experience within the assembly operation on a unit, which could lead to a curvilinear projection as in the other cases. To carry this line of reasoning a little further, it may be argued that even within an operation there are sub-operations, sub-sub-operations, etc. each having its peculiarities, leading to different rates at which experience can be gained. In other words, the main operation representing an aggregate of these sub-operations might produce curvilinear trends depending upon the different rates of improvement for each of these sub-operations. A study undertaken at the University of Iowa, where a punch-press operation was dissected into sub-operations (which were referred to as therbligs), and learning patterns for different individuals for each therblig studied, seemed to indicate different rates of improvement for the different therbligs. If so, the projection for the entire operation is likely to be curvilinear, although the chances of offsetting rates might produce a quasi-linear trend. Of course, the curvilinearity for each

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7/

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72 operation might be insignificant by itself; however, when several operations are aggregated the total labor curve might be significantly affected. Another inconsistency which can be pointed out pertains to the dependent variable. It is not uncommon to find direct labor hours plotted against cumulative production to arrive at the linear projection. Neither is it uncommon to find total costs being used in place of direct labor hours. Sometimes even man-hour cost per unit, or direct man-hours-perpound (as often used in the airframe industry) are represented on the ordinate. In other words, several different variables have been used, depending upon their suitability at depicting a straight line projection. But, then, total direct labor hours are not the sam.e as direct labor cost or total unit cost. They do not necessarily have an absolute relationship with direct labor cost, and certainly not with total cost. For example, if an incentive wage payment system has been employed, it might very V7ell be that the decrease in labor hours would be offset to a considerable degree by the increase in the labor rate to indicate no marked difference in the labor cost. Or referring back to Table II-II, the rate of decline in labor costs for increased output (a 70 per cent rate) is not the same as the rate of decline for total cost, as indicated by column 4 of the same table. Thus a decline in production time does not necessitate a proportional decline in labor cost or total cost, since a perfect correlation between direct labor hours, direct labor cost, or total cost cannot be generalized a priori. Hence, if a linear function results from using one of the above as the dependent variable, a curvilinear function may be the result if the

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73 other two are plotted. The point being brought out is that the experience curve "theory" with its linearity assumption has a nebulous definition for one of its determinants, a point which has hardly ever been discussed or criticized in current accounting literature. A question which often emerges in discussions concerning the learning "pattern" is : why is it that the constant percentage applies only to doubled quantities and not to tripled or quadrupled quantities? Is there something "inherent" in production processes that just leads to a certain percentage decrease every time quantity is doubled? True, it is often observed that when production data are plotted on logarithmic paper, one can derive a straight line with the help of statistical tools such as determining the line of best fit with the help of the least-squares method, as pointed out earlier. But is there any reason that production data might not be such that there occurs a constant rate of decline for tripled quantities? Assume the data hypothesized in Table II-III. This table has been so constructed as to indicate an 80 per cent rate of decline for tripled quantities. However, a straight line is projected when the information is plotted on logarithmic graph paper as indicated in Figure II-9. The reason for this seemingly peculiar result once more lies in the construction of logarithmic scales where relative changes are indicated. The distance between units one and three is the same as between three and nine, or between nine and twenty seven, reflecting proportional changes. Thus, what can be referred to as an 80 per cent experience rate for tripled quantities is also an 86.8 per cent per cent rate of decrease for doubled quantities. This indicates that what can be expressed by a rate of decline

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74 TABLE II-III Cost Data Signifying Constant Rate of Decline for Tripled Quantities Unit Number

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75FIGURE n-9 CONSTANT RATE OF DECLINE FOR TRIPLED QUANTITIES AS PROJECTED ON LOGARITHMIC-GRIDS Cumulative Production

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76 for tripled quantities. However, a straight line is projected when the information is plotted on logarithmic graph paper as indicated in Figure II-9. The reason for this seemingly peculiar result once more lies in the construction of logarithmic scales, where relative changes are indicated. The distance between units one and three is the same as between three and nine, or between nine and twenty-seven, reflecting proportional changes. Thus, what can be referred to as an 80 per cent experience rate for tripled quantities is also an 86.8 per cent rate of decrease for doubled quantities. This indicates that what can be expressed by a rate of decline for a tripled or quadrupled quantity of production can as well be expressed in the conventional manner as a rate for doubled quantity. The above analysis does not invalidate the hypothesis that production data can appear in forms other than the linear logarithmic type, neither does it ansxTOr the question posed before: is there something "inherent" in production processes which leads to the theorized linear form? It would be foolhardy to answer this question in the affirmative. Production data might take other forms, for example a constant rate of decline may be evidenced for equal quantities produced, or with each unit produced. It may be argued that it is "logical" to accept the contention that human beings can indicate an equal amount of improvement with equal opportunity for improvem.ent . Hovjever, a little thinkinii can upset the logic in the argument. In the first place what is "equal opportunity for improvement"? Even if this xcere true, that humans did improve an equal amount with a doubling of the original work done (a psychological hypothesis which would have to be empirically verified), why should this same contention apply to

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77 the experience curve which is affected by the complex business organism with its various components and functions. It is the contention of this study that there can be no a priori assertions regarding a linear pattern. The only thing that can be asserted is that the logarithmic scale, by bringing relative changes into the limelight, tends to generate a quasi-linear trend. However, the point to be noted is that there is no scientific reason for costs or production time to decline at a constant rate over an infinite range of production. The fact is that statistical and mathematical tools of approximation have to be utilized in order to generate a smooth linear trend and on this very ground the "theory" can be strongly criticized, a charge which has been undertaken in Chapter IV. From the above critique it will be noticed that at the very most, the experience curve "theory" is a rough approximation of production data as has been observed in special situations. The attempt at creating a universal proposition out of a simplified approximation might be one of the factors. '. which has led to the limited acceptance of the concept. The hypothesis that experience promotes efficiencies which lead to a decline in cost with increased production is still acceptable, but it might be dangerous to generalize that such declines take place by means of a constant percentage whenever quantities produced are doubled. It is not contended that the linear form cannot exist but that it may not exist. This does not imply that the linearity assumption should be wholly discredited and discarded, but that there should be an awareness of its implications. The linear form has considerable utility as a simplified

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78 approximation where analysis would not be possible, or extremely difficult; or where accuracy may be sacrificed for otherwise unavailable information. The above discussion was undertaken mainly because accounting literature is completely devoid of any mention of such peculiarities. Most of what has been written on the subject can be labelled as sim.ple propaganda that attempts to paint a rosy picture of how all the accountant has to do is "collect" two pieces of production data, and use logarithmic graph paper to draw a straight line experience curve, as some kind of a simple cure-all, To reiterate, it is not contended that the linearity assumption is useless, for it has a function to perform. It can be accepted as an approximation for purposes of simplicity , only when its peculiarities are properly understood.

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79 FOOTNOTES Chapter II 1. M. A. Reguero, An Economic Study of the Airframe Industry , Air Materiel Command, Wright-Patterson Airforce Base (Dayton, Ohio: October, 1957), p. 213. 2Ibid . 3. T. P. Wright, "Factors Affecting the Cost of Airplanes," Journal of the Aeronautical Sciences , III (February, 1935), 122-128. 4. Ibid ., pp. 124-125. 5. S. A. Billion, "Industrial Learning Curves and Forecasting," Management International Review , VI (1966), 68. 6. J. R. Crawford, "Learning Curve, Ship Curve, Ratios, Related Data," (Burbank, California: Locklieed Aircraft Corporation, n.d.). 7. H. Asher, Cost-Quantity Relationships in the Airfram,e Indus try , R-291 (Santa Monica, California: The Rand Corporation, July 1, 1956), pp. 15-46. 8. Publications by J. R. Crawford have been mentioned in the Bibliography. 9. J. R. Crav/ford and E. Strauss, Crawford-Strauss Study , Air Materiel Command (Dayton, Ohio: 1947). (Not reviewed by this study. 10. P. B. Crouse, "Projecting Labor Loads in Aircraft Produc-. tion," Aero Digest , XLIII, No. 4 (October, 1943), 216-218, 242-243. 11. A. B. Berghell, Production Engineering in the Aircraft In dustry (New York: McGraw-Hill Book Company, Inc., 1944), Chapter 12, pp. 166-198. 12. K. A. Middleton, "Wartime Productivity Changes in the Airframe Industry," Monthly Labor Review , LXI, No. 2 (August, 1945), 215-225. 13. G. W. Carr, "Peacetime Cost Estimating Requires New Learning Curves," Aviation , April, 1946, 76-77. 14. G. M. Giannini, "Aircraft Cost Control," Aero Digest , XXXIX (August, 1941), 187-1G9. 15. Po Guibert, Mathematical Studies of Aircraft Construction , Wright-Patterson Air Force Base, Dayton, Ohio. (Translation of P. Guibert 's Le Plan de Fabrication Aeronautique , Paris, 1945.) (Neither reviewed by this study.)

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80 16. E. Mensforth, "Airframe Production Part II," Aircraft Production , IX, No. 108 (October, 1947), 388-395. 17. W. Z. Hirsch, "Firm Progress Ratios," Econometrica , XXIV (April, 1955), 136-143; and "Manufacturing Progress Functions," The Review of Economics and Statistics , XXXIX (May, 1952), 143-155. 18. F. So Hoffman, Comments on the Modified Form of the Air craft Progress Function, R M-464 (Santa Monica, California: The Rand Corporation, October 4, 1950. 19. A. A. Alchian, An Airframe Production Function , P-108 (Santa Monica, California: The Rand Corporation, October 20, 1949); and Relia bility of Progress Curves in Airframe Production , RM260-1 (Santa Monica, California: The Rand Corporation, February 3, 1950). 20. Asher, op. cit ., pp. 24-26 21. A. D. Searle, "Productivity Changes in Selected Wartime Shipbuilding Programs," Monthly Labor Review , LXI (December, 1945), 1132-1147, 22. Reguero, op. cit ., pp. 213-240. 23. Asher, op. cit ., p. 191. 24. R. P. Zieke, "Progress Curve Analysis in the Aerospace Industry," unpublished thesis, Stanford University, 1962, pp. 93-95. 25. F. J. Andress, "The Learning Curve as a Production Tool," Harvard Business Review, XXXII (January-February, 1954), 87^88.' 26. W. B. Hirschmann, "Profit from the Learning Curve," Harvard Business Review , XLII (January-February, 1964), 125-139v 27. R. W. Conway and A. Schultz, "The Manufacturing Progress Function," The Journal of Industrial Engineering , X (January-February, 1959), 39-54. 28. R. R. Cole, "Increasing Utilization of the Cost-Quantity Relationship in Manufacturing," The Journal of Industrial Engineering, IX (May-June, 1958), 173-177. 29. E. B. Cochran, "New Concepts of the Learning Curve, " The Journal of Industrial Engineering , XI (July-August, 1960), 317-327. 30. Carr, op. cit ., pp. 76-77. 31. E. C. Keachie, Manufacturing Cost Reduction through the Curve of Natural Productivity Increase (Berkeley, California: Institute of Business and Economic Research, University of California, 1964).

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81 32. R. Wyer, "Industrial Accounting with the Learning Curve," The California C.P.A. , XXIII (February, 1956), 24-30; "Learning Curve Helps Figure Profits, Control Costs," N.A.C.A. Bulletin , X]{XV, Sec. 1 (December, 1953), 490-502; "Learning Curve Techniques for Direct Labor Management," N.A.A. Bulletin , XXXIX, Sec. 2 (July, 1958), 19-27. 33. R. Brenneck, "B-E Charts Reflecting Learning," N.A.A. Bulle tin, SL, Sec. 1 (June, 1959), 34; "The Learning Curve for Labor Hours For Pricing," N.A.A. Bulletin , XXXIX, Sec. 1 (June, 1958), 77-78; "Learning Curve Techniques for More Profitable Contracts," N.A.A. Bulletin , XL, Sec. 1 (July, 1959), 59-69. 34. R. B. Jordan, "Learning How to Use the Learning Curve," N.A.A. Bulletin , XXXIX, Sec. 1 (January, 1958), 27-39; "What's Your Progress Curve?" N.A.A. Bulletin , XLIII, Sec. 1 (March, 1962), 91-92. 35. B. T. Sanders and E. E. Blystone, "The Progress Curve — An Aid to Decision-Making," N.A.A .Bulletin , XLII, Sec. 1 (July, 1961), 81-86. 36. V. J. Shroad, "Control of Labor Costs Through the Use of Learning Curves," N.A.A. Bulletin, XLVI. Sec. 1 (October, 1964), 15-20. 37. A. E. BurroX';, "Use of Learning Curves in Contract Audits," The GAG Review (Winter, 1967), pp. 35-46. 38. Others have been mentioned by H. Asher, op. cit ., pp. 34-38. 39. T. F. Fowlkes, Aircraft Cost Curves: Derivation, Analysis Projection (Re-issue, Fort Worth: General Dynamics, August, 1963), p. 52. 40. The Rand Corporation studies, conducted for the United States Air Force, include: R-291, H. Asher, Cost-Quantity Relationships in the Airframe Industry , July 1, 1956, 191pp; P-IOS, A. Alchian, An Airframe Production Function , October 20, 1949, 16pp.; P-267, D. Novick, Use of the Learning Curve , November 9, 1951, 6p.; RM-456, K. J. Arrow, S. S. Arrov7, M ethodological Problems in Airframe Cost Performance Studies , September 20, 1950; RM-464, F. S. Hoffmann, Comments on the Modified Form of the Aircraft Progress Function , October 4, 1950, 12pp.; KM-260-1, A. Alchian, Reliability of Progress Curves in Airframe Production , February 3, 1950, 30pp.; RM-536, K„ J. Arrow, S. Arrow, and H. Bradley, Cost Quality Relations in Bomber Airplanes , February 6, 1951. 41. Included in the Stanford Research Institute Studies are: Development of Production Acceleration Curves for Airframes , September, 1948. Relationships for Determining the Optimum Expansibility of the Elements of a Peacetime Aircraft Procurement Program , December, 1949. A Method of Estimating Direct Operating and Maintenance Costs of Mili tary Transport Aircraft , June, 1954. (All attempts made by the author to secure these studies for perusal were unsuccessful.)

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82 42. Wright, op. cit ., p. 124. 43. Ibid ., pp. 124-125. 44. R. B. Jordan, "Vfnat's Your Progress Curve?" N. A. A. Bulletin , XLIII, Sec. 1 (March, 1962), 91-92. 45. Crawford, Learning Curve, Ship Curve, Ratios, Related Data , as reported by Asher, op. cit ., pp. 21-24. 46. H. R. Krocker and R. Peterson, "A Handbook of Learning Curve Techniques," The Ohio State University Research Foundation (Columbus, Ohio: 1961), p. 21. 47. Alchian, An Airframe Production Function , p. 4. 48. A. Alchian, Reliability of Progress Curves in Airframe Production , p. 30. 49. Ibid ., pp. 10-11. 50. Cole, op. cit ., pp. 174-175. 51. P. F. Williams, "The Application of Manufacturing Improvement Curves in Multi-Product Industries," The Journal of Industrial Engineering , XII (March-April, 1961), 108. 52. D. Schreiner, "The Manufacturing Progress Function: Its Application to Operations at IBM, Endicott," unpublished paper presented on behalf of International Business Machines Corporation. 53. E. C. Keachie, op. cit ., p. 83. 54. Hirschmann, op. cit ., pp. 125-139. 55. J. H. Siersema, "The Learning Curve," Cost and Management (May, 1960), pp. 186-200. 56. Letter dated September 26, 1967. 57. J. A. McGeoch and A. L. Irion, The Psychology of Human Learn ing (New York: David McKay Com.pany, Inc., December, 1961), pp. 1-34. 58. Ibid . 59. Ibid ., pp. 26-27. 60. L. A„ Barron, "Learner Curves Boost Team Output," American Mechanist , CII (December 1, 1958), 100.

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83 61. F. J. Powers, "Costs Strike Out with Learning Curve Incentive," Factory (October, 1961), 90. 62. J. R. Hadley, "Learning Curves on Log-Log Paper," Advanced Management , XV (April, 1950), 16-17. 63. L. Wertman, "Putting Learning Curves to Work," The Tool Engineer , XLI (September, 1959), 100-101. 64. For details on the choice of a term to signify the business "learning curve," refer to Y. Bhada, "The Experience Curve," unpublished master's thesis, Boxvling Green State University, August, 1965. 65. A set of data concerning a linear unit hour pattern has been used in this example for purposes of simplicity. The cumulative average hours could be used in place of the unit hours, without affecting the analysis. 66. For a good treatment of the subject, refer to Krocker and Peterson, op. cit ., pp. 4-7. 67. A sample of semi-logarithmic paper can be seen on p. 68. For the remainder of this study, it will be referred to as logarithmic paper. 69. Krocker and Peterson, op. cit ., pp. 6-7. 70. A. A. Alchian, "Costs and Outputs," The Allocation of Economic Resources , M. Abramovitz, et al . (California: Stanford University Press, 1959), pp. 23-40. 71. B. I. Maynard, "Mathematical Theory of Time Reduction Curves," Proceedings of the Fifth Annual Industrial Engineering Institute (University of California, 1953), p. 31. 72. Wright, op. cit ., pp. 124-125. 73. Crawford, op. cit . 74. Krocker and Peterson, op. cit ., p. 58. 75. Carr, op. cit ., pp. 76-77. 76. Wright, op. cit ., pp. 122-128. 77. Conway and Schultz, op. cit ., pp„ 39-54. '

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84 78. Relationships for Determining the Optimum Expansibility of the Elements of a Peacetime Aircraft Procurement Program , S.Pv..!., prepared for the Air Materiel Command, United States Air Force (December 31, 1949), as reported by Asher, op. cit., pp. 43-45. 79. Costs of distribution, general administration, etc., have been left out of the analysis in order to make the exam.ple simple to comprehend. Their inclusion would not affect the analysis in any significant manner. 80. Asher, op. cit ., p. 72. 81. Cochran, op. cit ., pp. 319-321. 82. R. M. Barnes, J. S. Perkins, and J. M. Juran, "A Study of the Effects of Practice on the Elements of a Factory Operation," Uni versity of Iowa Studies in Engineering , Bulletin 22 (November, 1940), pp. 3-86.

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CHAPTER III PROJECTING DYNAMIC PRODUCTION DATA Purpose and Organization of the Chapter What is the role of an accountant in the proper accumulation and dissemination of production data? How can accounting analyses concerning an entity be undertaken so that the impact of quantity produced on costs or production time be given adequate recognition? Partial answers to these questions have been attempted in the next few pages. Before any analyses can be conducted on the implications of experience gained on the quantity produced, it is essential to know how accounting data can be recorded, accumulated, and classified, for it is on the reliability of the data presented that interpretations and judgments are based. The importance of managerial accounting depends on the accountant's analytical judgment which, in turn, is based on his knowledge, experience, and the reliability of data available to him. For these reasons, it is extremely important to know the proper means of accumulating data and arranging the information in a manner susceptible to adequate analysis and re" liable interpretations. With this in mind, the first section of the chapter has been aim.ed toward indicating what dynamic production data implies and the proper means of accumulating such data. Special emphasis has been placed on the varied difficulties that may be encountered in the process of accumulation, and possible treatments for such difficulties have been indicated. 85

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86 The second section contains an exhaustive treatment of the possible patterns that have been and can be observed in dynamic production data projections. The varied forms have been illustrated with graphs, tables, and mathematical formulae wherever possible. Suggestions for the study of continuous production data, which have utilized variables other than the conventional variables — cost, production time, and cumulative quantity producedhave been commented on in the last section. It is necessary that the accumulator of accounting information be aware of the different possibilities in order to be able to adapt to different situations. For accounting information to be valuable, it has to be relevant, and the principle of relevancy can be satisfied only if all the possible alternatives are kno^m. Presenting the alternatives is what has been attem.pted in these last two sections. Accumulation of Accounting Data The dearth of literature on the subject of ascertaining the proper m.eans for collecting djmamic production data is almost unbelievable. Most publications advocating the use of production time-quantity relationships prefer to side-step the issue with an implied assumption regarding the availability of relevant production information. Only a few references touch on the procedure for accumulating data, and fewer still point out the difficulties that may be encountered. For this reason, a detailed investigation of these aspects has been undertaken in this section. The recording and accumulation of financial or quantitative data which can be utilized for discerning progress trends are undoubtedly within the realm of an accountant's job. The duty of collecting relevant informa-

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87 tion should fall squarely on the shoulders of the accountant, to whom the task of gathering data on production time or costs is by no means a new duty. Whether an accountant should be proficient enough in the use of sophisticated statistical and mathematical tools, or should these details be left to other "specialists" such as the industrial engineer is a debatable question. However, there is no doubt that the responsibility for accumulating the relevant details should be placed in the hands of the cost accountant. What should be the proper procedure for dynamic data collection? The usual simplified answer, implied by most authors, has been used as the starting point to lead into a discussion on the difficulties encountered in the process of accumulation. In the first place, determine whether the product or firm is susceptible to the impact of experience. In other words, is the nature of the manufacturing process such that the effect of experience gained with increased production could significantly affect the production time or cost of subsequent units produced? The implication is that if, for a firm or a product, the reply is negative, one can forget about the effects of experience, and use conventional accounting procedures. However, what is not indicated is that an answer to the above question cannot be supplied unless and until a thorough investigation has been undertaken to determine the impact of experience. It would be difficult to attempt an a priori judgment on whether the implications of experience are significant for inclusion in accounting analyses. For example, Frank Andress listed five industries, the products of

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which could profitably utilize the experience curve, and noted that a priori, a few other industries would find the implications of experience "of little value." This latter group included basic chemicals, plastics, petroleum refining, and manufacture of certain kinds of standard toys. Andress' claim was strongly refuted by Winfred Hirschmann, who presented empirical findings to support the contention that the effect of experience could be definitely observed in all the products and processes listed by Andress in his "of little value" group. Some form of an empirical investigation must be undertaken to ascertain whether a production process generates experience ^-^ich could affect data used for decision making. The next step advocated is to obtain the relevant data and make the necessary calculations. This is easier said than done; and yet, how many references can be quoted which merely state this requirement, and then go on to explain routine applications, assuming availability of accurate data. T%^nat exactly is "data"? How can its relevancy be ascertained? How does one go about obtaining this all-important ingredient? A composite answer to these questions usually im.plied is to determine the labor hours or the cost per unit as production takes place, and plot these data on logarithmic graph paper. In the first place, it would be important to define the "unit of production." In most cases, this would not be a difficult problem, for the unit of output may be readily identifiable. However, several problems of identification can, and do, arise. One such practical difficulty that has been observed pertains to the determination of the status of a product. Can a product, on which production has started, be considered new, or is

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89 it merely a variation of a product manufactured previously? This author's experience may be pertinent in illustrating the problem. An order was received from a major tire manufacturer for assembling a certain quantity of a special truck body. The customer indicated several specifications and details for assembly to the engineering department of the body construction com.pany. However, similar units were being assembled at that very time for another tire manufacturer , and although there were several variations between the two assemblies, there were considerable areas which were almost identical. The assembly crews that had worked on the earlier assembly were also to work on the new body, but with a few new workers introduced into the crews. The question that arose x^7as, should the new order be considered as a continuation of production or be treated as a new product? In a situation such as this, the accountant would have to seek the opinion of the industrial engineer or some other specialist who has a better knowledge of the production process. In the above situation , opinions were divided between the production manager, industrial engineer, the engineering department, and the shop foremen. The intensity of the problem was such that no decision could be made for purposes of considering the dynamic relationship. A corollary of the above problem is another knotty situation. I'lhich unit should be considered as the first unit produced? In some cases prototypes might have been built, or sample batches manufactured. Should these be considered as units produced, or should they be left out of the analyses? In most cases, prototypes or sample batches are produced with the

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90 help of special processes which are usually different from the production processes used in regular production. If such be the case, experience gained in their production may be left out of analyses. However, the inclusion or exclusion would have to depend upon the particular circumstances, and the criterion of relevancy would have to be utilized. Another case which is conceivable is where production of a few units might have been scattered over a long period of time. For example, one unit might have been produced six months back, another unit four months earlier, a third unit only a m.onth ago. Should these be considered as units produced, or should the unit under present construction be considered as the first unit? Once more the answer would have to be determined under the concept of relevancy, depending upon the degree to which transfer of experience could take place between the units produced. Yet another problem is encountered with partially completed units which might be in inventory. Here, the accountant's equivalent units concept can be profitably employed. However, what about fully or partially completed units which are rejected or are to be scrapped. To the extent that these units and the requisition of experience, they should be recognized adapting conventional procedures used, such as those for process cost accounting. If the output consists of joint products, conventional accounting treatment could once again be applied for calculation of units produced. Regarding labor hours or costs, it should be noted at the very outset that reference is to actual amounts observed, and not to any estimated figures. The danger in using estimated am.ounts is extreme, and such figures

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91 can be used only as rough approximations, and only if the user is completely aware of the dangers involved. Often, it might not be possible to identify actual labor hours with individual units produced. For example, in the case of multi-product manufacture, total labor hours or costs may be collected for batches or lots of several units, in which case only an average can be used to identify the labor hours expended on each unit in the lot. In such cases, lot aver3 ages can be used instead of individual hours for each specific unit. Ascertaining the unit labor hours, or the costs per unit, could present several difficulties. Considering the problem of labor hours first, an initial problem might arise in the differentiation of direct labor from indirect labor used. Although normal accounting definitions can be utilized to differentiate between the two categories, the validity of times charged to direct or indirect labor would always be questionable. However, once again conventional accounting definitions can be utilized, with minor variations, if necessary. Rolfe Wyer illustrates the difficulties involved in the accumulation of direct labor hours with examples regarding three cost elements: machine set-up, production inspection, and process operations. His point is that accountants often include these items under direct labor hours; and although each element might involve experience, there are certain characteristics which can significantly affect analyses if proper care is not taken. For example, where inspection is concerned, 100 per cent inspection might be undertaken for the first few items; whereas, only about 5 per cent inspection might take place nearing the end of the production run.-^ This m.ay

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92 indicate a completely different rate from other constituents, such as assembly labor, and hence its inclusion might introduce instability in the data. Another major problem is that of "attaching costs." If a job order cost system is in effect, the process of accumulating costs of assembly might not prove difficult, for a job order sheet could accompany each unit or lot as it passed through the different asembly operations. However, the question of machined parts is quite different. Some of the parts used for assembly purposes might be bought from outside, others might be produced at the plant, still others might be partially worked on or assembled in the shop. Should the time spent in the shop be included in the total labor hours figure or should machining be looked upon as a separate operations and costs separately collected? This question could arise provided the hours can be directly allocated to the units. But in most production situations, varying lot sizes, varying lead times, and varying schedules make it difficult to associate specific production quantities with the end product. Some components may be produced in relatively large quantities in initial lots, or lots may be split in the process of production. Some parts may be produced in the shop initially, and bought from outside suppliers later on. How should these problems be dealt with by the accountant? Two solutions to this problem of aggregation have been supplied by Conway and Schultz. One method is to time phase the data and add all the values making up a specific accumulation of the finished product. Another alternative is to accumulate each item cost at its cumulated production, and arrive at the total labor hours through simple aggregation of each unit of production.

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93 The experience of this author seems to indicate that the latter solution is more practical and reliable. The only difficulty that would be encountered is that the aggregation procedure is liable to generate a curvilinear trend for as indicated in Chapter II, aggregation of functions involving different decline rates is likely to be nonlinear. However, there is no reason that a curvilinear trend cannot be used, and therefore separate functions may be derived for different operations and plotted on the same graph according to their cumulative production number, and the total labor hours curve derived by a simple addition of all different operations at the particular production unit. An example of such a function xras shown earlier in Chapter II. Wherever machined parts or other distinct groups are manufactured in lots, data on such lots should be kept separate and time taken should be charged to assemblies using these parts on a first-in first-out basis, rather than on an average basis. After all, the entire analysis is built on the influence of experience on quantities produced. As Wyer indicates: "The accounting profession by instinct and habit likes to average figures and hence obtain more representative answers. In the case of learning Q curves, this is a cardinal sin." Wherever possible, details on sub-operations should also be gathered and used. The degree of detailed information to be collected would have to be determined by the degree of accuracy necessary and the financial resources available for data collection. Using costs (total or labor) instead of labor hours as one of the variables introduces additional problems, more complex in nature than those mentioned above. In case of labor costs, an additional element of labor

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94 rate is introduced which may "serve to mask production progress in terms 9 of fundamental resource consum.ption." It would be more advisable to segregate the effect of wage rates by using labor hours, and then to introduce the element of dollar rates, if desired. Using total costs as a variable would necessitate the inclusion of all costs, material, labor, and overhead. The results from aggregating all costs are more liable to collection difficulties, and unless the effect of experience on all three types are separately determined, and consequently aggregated, a total cost projection might prove hazardous for decision-making purposes. A total cost function, arrived at by aggregating individual elements was illustrated in the previous chapter. Further discussion on the material and overhead projections has been undertaken in Chapter V. The importance of accumulating representative, and hence reliable, data cannot be overstressed. This would necessitate a careful scrutiny of existing accounting procedures for established products, or the installation of an adequate system for a new product, if data for studying the impact of continuous production on quantity produced are desired. It could be that the existing system is adequate for generating the information needed, or it may be that some changes might have to be introduced, such as details in foremen's reports not undertaken previously. For example, this author was supplied data that indicated significant variations in the course of an investigation. On closer examination, it became evident that the shop foreman, when reporting worker-time spent on individual units, was not very oarticular on which unit he indicated the time, as long as he could

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95 vouch for each worker's eight-hour day. On being explained the need for proper information, he kept a record to indicate the exact time taken on each unit, which aided analysis considerably. An important point to be considered is whether extraneous factors are involved which might influence the reporting of data. For example. Billion observed that the presence of wage incentives often led to re10 strictions of output and inaccuracies in time recording. An aspect of reporting which is seldom undertaken is the highlighting of factors which could explain certain trends. Although quantitative data might be presented, it is equally important that qualitative factors affecting production be reported to facilitate better analysis. Williams has suggested that factors relating to changes in production efficiency be recorded when they occur. Examples of such factors are changes in personnel, m-anufacturing methods, materials handling techniques, complexity of design, quality of raw materials or components, production rate, or any other changes that might affect the labor cost of the product. A history of each product, indicating changes and other influences, should be kept along with the quantitative information. A complete understanding of the problems involved and peculiarities attached to a product could supply considerably more information than just the quantitative data. Proper decisions cannot be made without all the relevant information, and the quantitative figures cannot supply all data that can be considered relevant. Once the information has been collected, the question arises: what can be done with it? As stated earlier, the production data can be plotted

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96 on graph paper to observe the trend, or mathematical formulae can be used to exterpolate the data for forecasting and control purposes. The next section has been entirely devoted to the patterns that could arise in dynamic production data analysis. It should bo noted that the smooth curves indicated do not necessarily imply that the plots follow a perfectly smooth path. As a matter of fact, the chances of getting a smooth projection are almost negligible. However, the smoothness is artificially produced to aid the process of interpretation and decision making. Similarly, a "linear" projection is artificially derived from the scattered information by using statistical tools. Kow a straight line can be dratm from a mass of scattered points will be explained in the next chapter. Possible Patterns in Dynamic Production Data Projections After the production data have been summarized in the form of a schedule, they can be studied for possible trends to aid management's planning and control functions. Graphical means can be utilized, along with other statistical and mathematical tools to prepare the data for more efficient analysis. The varied forms that production data might taken, when graphed, have been indicated in this section. An attempt has been made to bring together different possible forms which dynamic production data might take, of which the accounting profession has not sho\^m an awareness, with 12 the hope that this could aid accounting analyses. A. Constant rate of decline for unit hours The first case deals with a situation which is often presented as the "learning curve theory" by some, and considered a "version" or an

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97 "interpretation" of the "learning curve theory" by others. Assume the hypothetical data presented in Table III-I, in which the second column indicates the labor hours for the corresponding unit in the first column. Thus the first unit is assumed to be produced in a thousand hours, the fourth unit is approximately 640 hours, and so on. On closer examination, it can be noticed that the individual unit labor hours are declining at a constant rate every time production is doubled. Thus, when plotted on logarithmic paper, the unit hours line can be projected as a smooth straight line, as can be seen in Figure III-l, where AB represents the unit hour curve. In such a case, the cumulative average, which can be arrived at by taking the cumulative total (indicated by the third column) at any level of production and dividing that total by the number of units produced, shows a slow decline at the initial stages, but gathers momentum as production continues. Thus, the cumulative average curve appears as shon-m by the curvilinear projection AC in Figure III-l. It should be noted that, after a certain level of production (around forty units in this case), the cumulative average curve runs parallel to the unit curve. By plotting the cumulative total figures, a slightly curvillinear upward sloping projection AD can be evidenced, which has been broken up in the figure for lack of sufficient number of vertical cycles. This form of projection is often referred to as the "airframe interpretation," as several airframe companies found that empirical data seemed to fit this pattern better. They found a constant decrease in labor requirements embodied in individual units throughout the range of production, as production was doubled every time. This meant a slow decline in the cumula-

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98 TABLE III -I Production Data Indicating a Constant Rate of Improvement for Unit Hours Unit Labor Cumulative Cumulative Number Hours Total Average 1 2 3 4 5 6 7 8 9 10 15 20 25 30 40 50 75 100 250 500 1,000 1,500 2,000 2,500 3,250 4,000 5,000 5,500 1,000.00

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9? + O CO < — I z \

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100 tive average in the initial stages, which quickened after some time, and finally steadied at a constant rate, resulting in a straight line unit hours curve and a humped cumulative average curve, as sho^-m in Figure III-l. The linear unit hours curve can then be defined by the mathematical 13 formula: F -S U = -^ = FN where U indicates the unit hours, F represents unit hours for the first unit, N is the number of units, and S is the exponent of the slope of the curve. Details regarding the derivation and m.eaning of the exponent of the slope S have been discussed in Chapter IV. The equation for the cumulative average would then be: F C F 1 + 9 CA = Y + s ^ or CA = Y + S N ^ where CA'stands for the cumulative average, and all the other symbols are the sam.e as those defined above. The cumulative total can be derived by using the formula: CT = ^ U -^ S 1 + S where CT stands for the cumulative total and all the other symbols are the same as before. B ^Consta-nt rate of decline_f or j:umu _ l^ ^ , ^°^^ , ^ , This pattern deals with a production situation which is also considered a variant of the "learning curve theory." In this case the nature of the production data is such that when cumulative averages at different levels of cum.ulative production are plotted, the resultant function is linear on logarithmic paper. Table III-II deals with another hypothetical

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TABI£ III-II PRODUCTION DATA INDICATING AN INITIALLY FAST RATE OF IMPROVEl^lENT FOR UNIT HOURS 101 Unit

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102 situation, and indicates the unit labor hours along with their corresponding cumulative totals and cumulative averages at different levels of production. When plotted on logarithmic graph paper, the data appear as in Figure III-2 where the unit labor hours function AB indicates a relatively fast decline in the initial stages of production, but slows down to a steadydecline as production continues. On the other hand, when the cumulative average hours at different levels of production are plotted, a straight line projection is the result, as indicated by the linear function AC. It will be noticed that after the twentieth unit or so, the unit curve runs almost parallel to the cumulative average line. An interesting thing to note is that the cumulative total line AD is an upward sloping linear projection, and once more has been broken up for lack of space. The linear cumulative average function can be expressed mathematically as: CA = ^ , or by CA = log F S log N where, as in the previous situation, CA stands for the cumulative average, F is the direct labor hours for unit number one, N is the number of units for which the cumulative average is being located, and S is the exponent of the slops of the line. As the line is always downward sloping, S will always be negative. It will be noted that the right hand side of the equation is the same for the cumulative average in this case, as it xv'as the unit hours curve in the previous case. Thus, CA = FW"^ and U = FN"^ . This does not m.ean that CA = U, for CA can be equal to U only at unit number one, or at F. The FN" merely indicates a linear regression on logarithmic

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/d73 b b +

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104 scales, which is commonly referred to as a Y = ax function, and whether this projection fits the cumulative average curve or the unit hour curve would have to depend upon each particular case, and upon the judgment of the accountant or the statistician. ' Either CA can be expressed as a linear function, or U can be so defined, or neither of the two may be linear. Hov/ever, if either one is linear, then the other would necessary be curvilinear. If the cumulative average line is taken to be linear, then the cumulative total line is expressed by the formula: CT = CA X N; or CT = FN*^-'" ^^ where CT stands for the cumulative total, and the other symbols are as stated earlier. The labor hours for a particular unit can then be expressed by the equation U = F 1,(1 S) _ ^^ . ,) (I S) Where U denotes the unit man hours. However, the above vormula is not very convenient to use, especially when U is a large figure, for longer and longer logarithms have to be used. Fortunately, there is an approximation which has proved reliable enough:" U F (I S) " (N 0.5)s Symbols are the same as those used above. It should be remembered that the above mentioned formulae can be utilized effectively only when the production data establish a pattern whereby the cumulative averages decline by a constant percentage at doubled quantities, and the direct labor hours per unit decrease at a relatively

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105 faster rate during the early stages of production but gradually approach a constant rate of decline as production continues. C. Constant rate of decline for lot averages I^Jhere the individual unit labor hours are observed to be erratic, it might be almost impossible to determine a trend on which reliance could be placed, if unit hours were to be used as a basis for decision making. It is conceivable that due to stoppages (even if they be of a short duration) the curve may follow a "scalloped" pattern. To avoid this, a lot average may be ascertained which, when plotted, may provide a reliable basis for forecasting and control. Table III-III provides hypothetical data for the first thirty units of a product xchich were produced in identifiable lots of varied sizes. The first three columns in Table III-III present the labor hours for different units, and their corresponding cumulative averages. The other four columns present the lots into which the units can be identified, the units per identified lot, the average hours for each lot, and the unit number at which this average can be plotted. The data for the individual units, as indicated by the first two columns, when plotted, appear as in Figure III-3, which can be considered a "scalloped" curve, for distinct breaks can be observed. A scalloped curve is not an uncommon representation, for engineering or product changes or considerable lapse of time between lots could lead to such a pattern. However, when the lot averages are plotted, a good linear projection ensues, as can be seen in Figure III-4, where the straight line AB is the unit average curve, and the curvilinear projection AC is the cumulative average curve

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106 TABLE III -III Production Data for Units Produced in Identifiable Lots Unit Labor Cumulative Lot Units Lot Av. Unit No. Number Hours Average Number in Lot Hours Average 1

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/OS: o» / / O ' I % < f o U-+/

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109 which turns out to be a smooth but a humped projection in the initial stages, which straightens out and becomes parallel to AB as production continues. This method of plotting lot averages and using the unit average or lot average curve in place of the unit hours curve has proved quite reliable for some airframe manufacturers. Whenever definite lots can be identified and it can be observed that deviations are significant for individual units within the lots, the alternative as presented in this case can be utilized. D. Initial hump and constant rate of decline This case deals with a special situation which was indicated by a study undertaken at the Stanford Research Institute. The curve indicated in Figure III-5 is the unit hour curve which has a very slow initial decline, but gathers momentum, and approaches a linear asymptote as production increases. Since the unit hour curve is concave to the point of origin, the cumulative average curve would also be concave, but has not been shown on the graph, as it does not affect the analysis in any manner. In Figure III-5, the curve is shown approaching the linear asymptote and, although theoretically it can never touch the asymptote, for all practical purposes the curve can be considered to converge with the asymptote. In such a situation, it has been suggested that a "B" factor be used where "B" is a constant expressed in terms of units. In other words, data can be shifted to the right until a linear unit hour projection is obtained. Thus the unit hours at unit one could be plotted at, say, unit four, in which case the hours for unit two would be plotted at unit five, and so forth, indicating a "B" factor of three units. In this manner, a linear

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//o

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Ill projection can be obtained by ascertaining the proper "B" factor which indicates the amount of experience expressed in units, which is assumed to have been transferred from earlier production. This "B" factor represents a certain quantity which might have been produced before, or some experience which might have been gained on similar operations. Aggregatively this experience might be worth an equivalent of what might have resulted from having produced the specific quantity of units represented by the "B" factor during regular production. The unit hours under the above interpretation can be expressed mathem.atically by the equation: U = F (N + B)^ where F is the constant direct labor hours for the first unit when B is equal to zero, N is the unit number, B is the constant, and S is the negative exponent of the asymptote toward which the unit curve approaches . The asymptote has been indicated in Figure III-5 by the dotted line. The cumulative average curve would then be expressed by the equation: F q CA + Y+~S ^'^ + ^) The formula for the cumulative total curve would be: The symbols would be the same as before, with S being a negative exponent. E. The "inverted S" pattern A peculiar pattern was noticed by Gardner W. Carr of McDonnell Aircraft Corporation, which was reported by him in the April, 1946, issue of

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112 Aviation . The "S" shaped curve observed by Carr has also been evidenced by others, including E. B. Cochran, who asserted its applicability in a curve may start with a hump signifying a slow rate of improvement, but after a certain point is reached (which he stated was between ten and twenty units for airplane production), the rate of improvement tends to increase rapidly, unlike the Stanford Research Institute's initially humped projection for the unit hour curve. Carr's thesis was that another point would be reached (between the hundredth and three-hundredth plane), beyond which the curve would flatten out. Once this point is reached, m.an hour costs would slowly approach optimum. The curve then takes the shape of an "inverted S," as shown in Figure III-6. A straight line indicating a constant percentage decrease has also been drawn in the graph so that the nonlinearity of the S curve can be better visualized. Cochran has also supplied evidence to support the existence of an "inverted S" curve pattern: Considerable actual experience . . . indicates rather clearly more of an S -curve than a linear function . . . [which] has been roughly confirmed by informal review of several companies' recent cost experience, and appears compatible with some of the data published on World War II airframe costs. ... It is further supported by the frequent comments by production personnel on the need to recognize a trend for costs to flatten out comewhat as unit output gets larger. 19 He goes on to shov; how an S-shaped curve can be constructed in five "simple" steps. However, several assumptions and arbitrary values to be used in the construction process indicate doubtful reliability for the procedures suggested.^""

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//3 > k 3 O 4!un J8d SJnoH Joqoi

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114 F. A convex projection In an earlier discussion on the linear assumption, it was indicated that when total cost is plotted against cumulative production, the curve tends toward convexity, due to the fact that cost elements with a slower rate of improvement tend to flatten the total cost curve (refer to Table I-II and Figure 1-7). Similarly, if only labor hours are used as a variable, the curve might still be convex to the point of origin, due to labor on different types of operations being brought under the analysis (refer to Figure 1-8). The projection may gradually level off or flatten out. In a Rand Corporation study, Harold Asher has well substantiated this hypothesis with the help of empirical data. Asher carefully explains how and why an experience curve gradually becomes flatter as production increases. After considerable analysis, he concludes that "... the conventional linear progress curve is not an accurate description of the relationship between unit cost and cumulative output. Beyond certain values of cumulative out21 put, both the labor and the production cost curves develop convexities." Hence a convex curve is a definite possibility. G. A constant rate of decline for equal quantities This situation involves data which may truly be considered "unusual." For example, the hypothetical figures in Table III-IV represent a situation where there is a constant rate of improvement per unit of product produced. Instead of labor hours declining by a constant percentage with every doubled quantity, the labor hours in this case are declining by a constant percentage with every equal amount of production, that is, V7ith the production of

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115 TABLE IIIIV Production Data Indicating a Constant Rate of Improvement for Equal Quantities Produced Unit Number 1 -2 3 4 5 6 7 8 9 10 11 12 Labor

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116 every unit. Tv^hen plotted on log-log graph paper the projection appears curvilinear, concave to the point of origin, as seen in Figure III-7. But, when plotted on semi-log graph paper, the function appears to be linear, as sho\TO in Figure III-8, which can be expressed mathematically as a y = ab'^ or log Y = log a -h X log b function. Therefore, when the rate of decline is constant for equal amounts of successive units produced, it is advisable to use semi-log graph paper instead of full-log to get a linear function. It should be noted that this case differs slightly from the initially concave unit curve mentioned earlier. Whereas on double logarithmic graph paper, the Stanford humped curve had a slight initial hump and the function straightened out into a linear projection for subsequent production, the hump does not straighten out in the present case, as the rate of decline stays constant per unit of production and not for doubled quanl^ities. The concavity on double logarithmic graph paper would continue as long as the constant rate for equal quantities produced continues. However, such a case would be unusual, and extreme care would have to be taken to validate the continuation of such a trend. H. Possible deviations from regular patterns A few deviations observed by Reguero and reported by him in his study An Economic Study of the Military Airframe Industry may be considered 22 as peculiarities which can arise under any pattern discussed thus far. Among the variations pointed out are three which have not yet been discussed. The first deviation is where a "leveling off" or a "bottoming out"

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i/y ^^v^^^^Unit Hour ^^ Curve ^ \

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Iff FIGURE in-8 CONSTANT RATE OF DECLINE FOR EQUAL QUANTITIES, PROJECTED ON SEMI-LOGARITHMIC GRIDS 10=1 4 5 6 7 8 9 10 11 Cumulative Production 12 13 14

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119 is observed. When, instead of labor hours declining with increase in production, it is observed that the time taken per unit suddenly turns constant, indicating no improvement with increased production, a leveling-off situation arises. This leveling off may be due to a com.bination of several factors such as sagging morale, boredom through monotony, shifting of good workers or efficient machines to other jobs, or the end of the production run coming in sight. A leveling off was observed by the Lockheed Aircraft Company on their B-17 at their Burbank plant, and their experience has been shown in Figure III-9. A similar leveling off was also observed in a study undertaken at the Boeing Aircraft Company. ^"^ In this study it was found that the leveling-off point was different for different aircraft, but there was sufficient evidence to support the contention that beyond a point the improvem.ent rate stops declining. It is conceivable that instead of merely leveling off, a curve might start rising. Reguero is of the opinion that there is a tendency for direct man hours per pound to rise, or "toe-up," as a program comes to an end. Most of the reasons mentioned for a leveling-off (with greater intensity, perhaps) can also cause a toe-up. Approaching the end of the production run, or a go-slow strike, or some union decision, could conceivably lead to a toe-up. However, as Reguero asserts, "whatever the reason for a toeup, it is not that the capacity for learning ceases or retrogresses, but 25 that less efficient means are used." An example of a toe-up curve has been shown in Figure III-IO, which was reported by the Boeing Airplane Company, Seattle, for their B-17.

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/2 o o o o o o o o o o ^OCfiOOOOOn FIGURE III-9 AN EXAMPLE OF A "LEVELING-OFF" CURVE: LOCKHEED, BURBANK-B 17 Cumulative Plane Number

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121 o o o o o 100=1 FIGURE m-IO AN EXAMPLE OF A "TOE-UP" CURVE: BOEING SEATTLE, B-17 LEARNING CURVE Cumulative Plane Number

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122 A "toe-doW situation is also possible, although its occurrence may be considered unusual. Figtire III-ll indicates the experience of Douglas Aircraft Company, Inc. in the production of their B-24 at Tulsa. In this case, a linear pattern was observed until approximately 500 units were produced, after which a steep decline was observed. A toe-do\m pattern was also noticed by North American Corporation at Dallas on their B-24. The reasons for this occurrence would be the opposite of those mentioned for the leveling-off and toe-up situations. Thus, better morale, continuation of the contract, fewer engineering changes, salvaging work from earlier units, etc., could lead to a toe-doxm pattern. I. No observable trend Finally, there can arise a situation where no trend can be observed from the data collected. This would also be an unusual situation if the unit has been properly defined, data have been accurately collected, and care has been taken to determine uniformity in the production operations. However, it m.ight be that the unit has several varieties which require completely different treatments. Or production can be accomplished in several ways and, whereas one unit is produced by hard labor, another may be produced on a machine, leading to widely varying direct labor hours being reported. Yet another explanation might be that data are not properly classified, with the result that improper charges are burdened on units other than the ones which should have received the charges. To illustrate, let us assume a company which builds yachts. All types and sizes of yachts can be built at the yard, from floating paradises built for movie stars and millionaires to dingy "it-will-do" types for

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/^3 o G O o o o

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124 college professors. Now, if data vere collected for all these different types under one group, the resultant relationship between labor hours and quantity produced would serve no useful purpose. The hypothetical labor hours per unit, as shown in Column 2 of Tabic III-V, when plotted, would appear as a meaningless projection as seen in Figure III-12« Hovjever, on closer examination it may be found that there are three distinct types of products wrongly classified into one group. It should be remembered that units within each group need not be identical provided there is a significant degree of similarity between units. A careful analysis of the production data presented in Table III-V, seem to indicate that three distinct varieties of the produce have been considered under this group. Vhen these varieties are differentiated and considered as different products, as shown in Columns 2, 3, and 4, of Table III-V, reliable trend lines can be observed for each of the three categories, as seen in Figure III-13, In the above example, there is an implied assumption that the production processes for the three groups are different. If not, a common basis could be established such as man-hours per pound, to conduct joint analysis. It is conceivable that a situation might arise whereby identical units can be produced by means of different production processes. Thus, among a group of widgets produced, some might have undergone certain operations on a machine, whereas others might have been hand assembled. In such cases, if direct labor hours were used as the dependent variable, it is important that similarly constructed units be graphed together, if any degree of reliability is expected from plotting the data.

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125

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in 100 Cumulative Production

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128 The possibility of inaccurate reporting can hardly be overemphasized. While conducting empirical research, the author of this study encountered extreme difficulty in assimilating data which could be accepted as reliable for research purposes. There is no doubt in the contention that unless proper care is taken to obtain accurate data, any decision made using inaccurate information could prove disastrous to the user. This subject will be referred to again several times during the course of this study. The possibility of a no-trend pattern cannot be ruled out. It is conceivable that even after all the necessary care and trouble, no possible pattern can be observed. In such a case, a rough approximation may be used with extreme care, and decisions made on such information should be limited as much as possible. However, a persistent study is likely to indicate some form of a representation which could be useful for planning and control purposes. Variations Suggested for the Study of Dynamic Data In this section, two approaches to the study of dynamic production data which involve variables in addition to those used in the previous section have been discussed. The first variation concerns the work of a Frenchman, P. Guibert, x
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129 Guibert's study Guibert's Le Plan de Fabrication Aeronautique was based on data taken from the French aircraft industry. It was originally published by Dunod, and later translated at the Wright-Patterson Air Force Base under the title Mathematical Sttidies of Aircraft Construction . In this work, Guibert presented an approach which differed from that used by Americans. He introduced the rate of production as a variable affecting unit labor cost, and asserted that the unit cost-quantity relationship approached a horizontal asympote when large quantities of units were produced. However, he expressed man-hour cost as a ratio of the cost of each unit to the cost of the number of units in process when peak production was attained. Man-hour cost was expressed as the ratio of the cost of each unit to the cost of Unit A. He defined A as A = aCK where a is the monthly production, C is the flow time per unit at peak production, and K is a parameter, the value of which is dependent on the rate of production and on the flow time, but which is close to unity. Thus he arrived at different functions for different rates of production, each approaching a horizontal asymptote after a considerable number of units were produced. Guibert's unit curves can be expressed by the equation: „ . ^^^ , (a-l)(a-m) (I-m) (A-I) ^ "" X(a-I)= A (I-m)(a-m) The above equation can be used for any rate of production as long as ra, a, and A are each a function of the rate of production. In the equation, y stands for the unit hours, m is the value of the horizontal asymptote, a is the cost at unit number one, and A denotes the number

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130 of units in process when peak production is attained. Due to the complexity of calculation and the curvilinear form proposed by Guibert, American industry has not accepted its applicability. Zieke bemoans this lack of interest and strongly implies that Guibert 's model might have considerable potential which could be researched. The Boeing 707 study Anand Garg and Pierce Milliman have suggested a means of incorporating the factor of design changes in dynamic production data analysis which was successfully tested by them on the Boeing 707 commercial jet transport 29 series. They reported significant improvement in man-hour estimates through the use of their modified formula on the 707 family of jets. The formula for the unit hour projection, as modified by the Stanford Research Institute's B factor, has been further modified by Garg and Milliman to take into consideration a new variable D, which represents the number of engineering drawings. The authors found that their modified formula resulted in much better estimates than those obtained by the usual linear function or the Stanford "B" curve. Due to the complex nature of the formula suggested by the joint authors, it has been presented in Aopendix B, rather than in the text itself.

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131 FOOTNOTES Chapter III 1. F. J. Andress, "The Learning Curve as a Production Tool," Harvard Business Review , XXXII (January-February, 1959), 258-259. 2. W. B. Hirschmann, "Profit from the Learning Curve," Harvard Business Review , XLII (January-February, 1964), 128-134. 3. P. F. Williams, "The Application of Manufacturing Improvement Curves in Multi-Product Industries," The Journal of Industrial Engineering , XII (March-April, 1961), 109. 4. R. Wyer, "Industrial Accounting with the Learning Curve," The California C.P.A ., XXIII (February, 1945), 29-30. 5. Ibid., pp. 25-26. 6. R. W. Conway and A. Schultz, "The Manufacturing Progress Function," The Journal of Industrial Engineering , X (January-February, 1959), 43. 1 ' Ibid., pp. 43-44. 8. Wyer, op. cit ., pp. 24-30. 9. Conway and Schultz, op. cit ., p. 53. 10. A. A. Billion, "Industrial Time Reduction Curves as Tools for Forecasting," unpublished doctoral dissertation, Michigan State University, 1960, p. 98. 11. William, op. cit ., p. 109. 12. For the remainder of this chapter labor hours have been used instead of costs, as one of the variables, for reasons indicated earlier. However, labor costs or total costs could be used if found advisable. 13. Most of the ma.thematical formulae expressed have been widely quoted, and hence no particular source has been acknowledged. However, for a more analytical treatment, including mathematical proofs, one may refer to A. B. Berghell, Production Engineering in the Aircraft Industry (New York: McGraw-Hill Book Company, Inc., 1944), Chapter XII. 14. B. I. Maynard, "Mathematical Theory of Time Reduction Curves," Proceedings of the Fifth Annual Industrial Engineering Institute , University of California (1953), p. 31.

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132 15. Berghell, op. clt ., pp. 177-178. 16. As stated in Chapter II, the original works were not reviewed as all attempts at securing the Stanford Research Institute publications were unsuccessful. ReviG--7G in the following works were referred to: R. P. Zicke, "Progress Curve Analysis in the Aerospace Industry," m^publishcd masters thesis, Stanford University, 1962; M. A. Rcgucro, An Economic Study of the Airframe Industry , Air Materiel Command, Wright-Patterson Air Force Base (Ohio: October, 1957); H. Asher, Cost-Quantity Rc3.ationship in the Airframe Industry , R-291 (Santa Monica, California: The Rand Corporation, July 1, 1956). 17. G. W. Carr, "Peacetime Cost Estimating Requires New Learning Curves," Aviation (April, 1946), pp. 76-77. 18. E. B. Cochran, "New Concepts of the Learning Curve," The Journal of Industrial Engineering , XI (July-August, 1960), 317-327. 19. Ibid ., pp. 323-325. 20. Ibid., pp. 317-327. 21. Asher, op. cit ., p. 129. 22. Reguero, op. cit .. Chapter XI. 23. E. 0. Weining, Improvement Curve Study , Boeing Airplane Company (Wichita, Kansas: August 11, 1949), p. 42. 24. Reguero, op. cit ., p. 228. 25. Ibid., p. 229. 26. Ibid., p. 233. 27. In spite of all possible effort, no copy of Guibert's work (including the French edition) could be secured. Hence, reliance has been placed on the review by R. P. Zieke, op. cit ., who has indicated special interest in the work. 28. This study agrees with Zieke 's observation, although for different reasons. This author believes that Guibert m.ay have accidentally pointed to a means of reconciling the Classical and Neo-Classical static economic analysis with a dynamic production function. However, no contention is to be implied from this observation, as this belief has not been researched, for it is believed to be beyond the scope of this study. 29. A. Garg and P. Milliman, "The Aircraft Progress Curve — Modified for Design Changes," The Journal of Aeronautical Engineering , XII (JanuaryFebruary, 1961), pp. 23-28.

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CHAPTER IV QUANTITATIVE AND QUALITATIVE IMPLICATIONS OF THE EXPERIENCE RATE The Purpose and Organization of the Chapter A question which could have been posed in the preceding chapter, but •which was deliberately postponed for a specific reason, has been discussed in the next section of this chapter. The question may be phrased as: after having collected the relevant data, how does one go about fitting a trend? That is, what are the statistical and mathematical implications of trend fitting for purposes of analyses? The reason for postponing an answer to this question may be stated in terms of this author's belief that it might be more relevant to know the types of models that can be utilized in order to avoid the common pitfall of necessarily expecting a linear logarithmic function, which is generally theorized in accounting literature. Knowing the varied patterns can contribution to a proper classification and accumulation of relevant data, and therefore, a more meaningful means — consequence relationship. To aid the research, a set of actual data, made available by a firm for a previous investigation has been utilized. Different patterns and statistical methods have been experimented with to indicate the factors involved in the usage of the statistical and mathematical tools. The place of subjective judgments in the fitting of trends has been investigated, and detailed analyses undertaken to arrive at results which have been considered interesting and quite consequential from the point of view of this study. The section following the above-mentioned investigation comments on 133

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134 the meaning and implications of the experience rate. Details regarding the slops of the function and the exponent of the slope for mathematical analyses have been provided. This is followed by a section on the significance of the experience rate or rates, v/herein an answer is provided to the question: "what can these rates suggest to the managerial accountant?" An area which has been neglected to a certain degree in the study of production time-quantity relationships, and which is capable of providing sufficient material for several research projects, is the subject of the final section. In this section, factors that determine the rate of experience or influence the rate in any manner, broken down into pre-production and during-production factors, have been enumerated. This vTriter firmly believes that a concerted effort in the direction of determination and measurement of these factors can prove extremely beneficial to business and industry. Considerable help from other disciplines such as psychology, business management, sociology, engineering, economics, and other allied fields, might have to be pooled for better results. An operations research approach can provide valuable information for firms and industries. This involvement of interdisciplinary knowledge is perhaps the major cause for lack of research in this area. For this reason, the study can claim only a modest accomplishment in the determination of factors affecting experience, for only a surface investigation was possible. However, a framework has been laid for further research, the need for v^hich is evident. Statistical and Mathematical Implications Deriving the line of best fit The discussions undertaken in the previous chapters have indicated

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135 the possibility of varied models that can be applied for dynamic production data analyses. The linear functions hypothesized by the learning curve "theories" have been considered as possible models, rather than as universal generalizations. However, this finding tends to introduce additional difficulties in the use of dynamic relationships for accounting analyses. If the linear hypothesis is unconditionally accepted, it is implied that one has merely to plot the cumulative production data for initial quantities produced, ascertain the line of best fit by visual inspection or with the help of statistical tools, and extend this straight line for forecasting and control purposes. In actuality, a different pattern might fit the data better, in which case it m.ay be advisable to derive a line of best fit which is curvilinear. The question that arises is: how can the accountant determine which model best fits the data? Should he assume a linear unit-hour curve and proceed to fit the hyperbola Y = AX"-^ to the individual unit hour date? Or should he draw a linear cumulative average curve and proceed to fit a curvilinear unit hour curve? Or should he use the humped unit hour pattern, or the inverted S curve, or the leveling-off convex model, or some other preconceived trend line? After all, from plotting the data, one merely obtains a scatter diagram of plots over the range of production considered. Is there any statistical method by which one can determine the most representative fit to be used? A detailed investigation into the experience curve literature resulted in no light being shed on the question, for a vast majority of the authors unconditionally accepted the linear logarithmic hypothesis. Hence,

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136 an answer to the question was sought through research into basic statistical treatises. The initial indication was that there was no such apparatus which could be considered "scientific," capable of indicating the superiority of one model over another. The general idea seemed to be that in regression analysis, one has first to hypothesize a particular arrangement and then a statistical line of best fit can be draxm in accordance with the preconceived hypothesis. The pattern should be selected through visual inspection, and only after the theory has been selected can the line of best fit be drawn. To quote an accepted authority on the subject: Fitting a trend by a mathematical formula does not, however, remove the subjective element from trend fitting. The statistician can vary the behavior of the curve by selection of the type of formula he employs. ... It remains true, therefore, that the statistician decides in advance, upon as objective and logical a basis as possible , what he thinks the trend ought to look like, and then selects the m.atheraatical method that \jill closely approxim.ate this result. 2 This observation made by Croxton and Cowden has been supported by various other statisticians, including Neter and Wasserman, who indicate that due to the involvem.ent of arbitrary factors in the interpreta.tion of a scatter diagram, such an analysis is bound to suffer from important 3 limitations . However, other sources seem to indicate the availability of means for determining the trend that can best fit a set of data. Dr. A, E. Brandt is of the firm opinion that one cannot and should not use a priori notions 4 regarding the possible trends. There are statistical tools which can be used in judging fits of various degrees, and such tools should be used in ascertaining the proper trends for it is possible to test any fitted function of any degree for goodness of fit. For example, G. W. Snedccor has

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137 presented a detailed example of how one can test the representative character of a fit. The reasoning behind the method used by Snedecor was initially expounded by R. A. Fisher, whose work is still looked upon as an authority (this is evidenced by the fact that the book has gone through thirteen editions). An unpublished paper by Brandt, written while associated with the United States Atomic Energy Commission as a biometrician, is a good example of how seemingly similar sets of data may involve different mathematical equations, and only a carefully conducted analysis can indicate the proper fit for a particular set. The decision of a linear versus a curvilinear model cannot be made independently from the mathematical implications of the data. One has to determine what the particular information implies. As a first step in fitting a function to a set of data, one can plot the observed values on rectangular graph paper, as even the most experienced statisticians have trouble visualizing trends in terms of non-uniform scales. Various degree curves can then be fitted. Thus, a zero degree curve results in most of the plot points falling around the mean of the sample. Therefore, a zero degree curve is a straight line running parallel to the X axis, A first degree curve is of the Y = a bX form, that is, a rising or a declining straight-line function on arithmetic grid graph paper. Such a straight line may be fitted by the method of least squares or orthogonal polynomials. A second degree or higher curve can be fitted by the method of least squares; but there is no separate test for the significance of the various degree fits. However, if a second, third, or higher degree curve is fitted by orthogonal polynomials, such fits can be separately tested for signifi-

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138 cance, and the function indicating the highest degree of significance should be selected as the best fit function. Now, transformations can be used to change non-linear data to a straight line form by the use of logarithmic or geometric scales. For example, if the data fits the formula Y = aX , or log Y = log a b log X, then a power function can be assumed and a linear model can be used on logarithmic scales. However, a concave function on logarithmic paper may be an exponential function of the Y = ab , or log Y = log a + X log b type which indicates a linear equation in log Y and the original values of X. This means that a linear function would result if the data were plotted on semi-log graph paper. A convex curve on full logarithmic paper may fit the equation Y = a + b log x better, in which case a linear function may be obtained on semi-log paper with the X axis representing the logarithmic scale and the Y axis marked in arithm.etic scale, and this function is often ref erred to as the logarithmic curve. Deriving a proper trend line usable for forecasting and control purposes may be accomplished in one of two ways. One method is to join all the plotted points by a line, starting from the y-intercept and connecting each succeeding scatter point. This may provide an uneven trend line; however, it would be most representative of the actual trend. Such a line could signify the dispersion within a set of data which could facilitate visualization by the human eye. Unfortunately, such a trend might prove disadvantageous for exterpolation purposes. To avoid this limitation, a smooth line may be statistically derived which would best fit the set of data. Such a smooth line m.ay be linear or curvilinear, and would pass through the scattered points to best represent the trend involved in the quantitative inform.ation.

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139 There are several says in which a representative smooth curve can be fitted--by mere sight-judgment, fitting a straight line using the method of least squares, or fitting curvilinear trends with the aid of polynomial computations. For non-linear data, it is possible to use a transformation which enables one to secure on equation in linear or first degree form wliich simplifies the arithmetic of fitting. The sightjudgment method is one wherein a smooth line that best fits the data is drawn without any statistical aid. The observer merely draws the line according to x\rhat he believes best represents the data. It is rather obvious that a considerable degree of subjective judgment is involved, and the possibility of "deriving" a preconceived slope is rather strong. Moreover, it would not be possible to evaluate the precision of any prediction for it would not be feasible to set confidence limits for such predictions. Hence, this approach may be considered adequate only if crude estimates are required. A slightly better method is to find the mean of the sample, to plot the mean at the calculated mid-point, and to draw a line passing through the point to indicate the trend in a manner which appears to be representative of the data. The more scientific approach to line fitting is the method of least squares, provided a linear model is evidenced from a casual observation of the scatter points. Although the method can be used to estimate both linear and curvilinear patterns, it is more commonly applied in connection with linear trends, for the procedure is extremely complicated when applied to curvilinear function fitting. By using this method, the sum of the vertical deviations of the observed values from the fitted line equals zero;

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140 furthermore, the sum of the squares of all these deviations is less than 9 the sum of the squared vertical deviations from any other straight line. An example of how a line of best fit can be derived, using the least square computations, has been illustrated in the next section and in Appendix C. If it is observed that the pattern is curvilinear rather than linear, polynomial equations can be utilized to fit or test such trends. The orthogonal poljmomial system of fitting curves provides several advantages^ by use of the polynomial equations, any type of curve can be adapted to the set of data. This leads to a considerable degree of flexibility and adaptability for a wide assortment of data. For example, a straight line can be dravm by using a first degree curve; a second degree curve leads to a parabolic function; an S-shaped curve would result from using a third degree polynomial, and so forth. The difficulties involved in hypothesizing a trend for a set of data, and fitting a smooth line to characterize that trend, can be appreciated only if they are witnessed in an actual situation. For this purpose, a set of data collected in the course of an empirical investigation has been used in the next section to illustrate the point. An implication regarding the recognition of a trend to which this writer has not seen any reference has also been tested in the next section. This is in reference to an extremely important question that often arises in practical situations: when can the accountant recognize a trend and hence start to fit a sm.ooth line? For example, should one wait until data on the first five units are available, or should one wait for more information? How much information is necessary before a reliable trend line can

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141 be fitted? There is no doubt that the smaller the sample used, the greater the likelihood of error through extrapolation, for a sufficient quantity of units has to be produced before the production process can be said to have "settled doi-m." But, when can production be considered as having settled do^m? It would be foolhardy to designate an absolute quantity as the number at which the accountant can start fitting the trend. Only the particular circumstances surrounding production, and a constant observation of the scatter as more information is made available can indicate when the actual line fitting can be undertaken, as will be seen in the next section. Experimentation with actual data In this section, an attempt has been made to indicate the implications involved in "fitting" a trend to a set of actual data. The figures used for purposes of analyses were obtained from the industrial engineer of a special truck and body construction plant located in the m.idwest. The inform.ation relates to the construction and assembly of a special povjer-gate completed by the company over a period of two years. It should be noted that the information was not collected especially for this study, but had been accumulated for some other analysis by the industrial engineer. Therefore, no claim can be made for the reliability and accuracy of the reported figures. However, it should be pointed out that the set of data has not been used for purposes of validating hypotheses, but primarily to serve as an example of what is involved in the use of statistical tools. Hence the doubtful element in the acceptability of the data would not affect the analysis in any conceivable manner. Table IV-I presents the assembly times for the first nineteen units,

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142 TABLE IV-I Assembly-Time Analysis for the First Nineteen Units Produced Unit

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143 arranged in their chronological order of completion, along with the ctimulative averages and cumulative totals at each level of production. On the basis of the information presented, hox^7 can the accountant determine the trend line? As explained earlier, the data can be plotted on arithmetic or logarithmic grid graph paper, and the results would be a scatter diagrams as seen in Figure IV-1 and Figure IV-2, respectively. In these figures, the labor hours per unit have been plotted at their completion number. As pointed out earlier, it is important that the initial units be plotted on arithmetic graph paper first, for a careful consideration of the plain graph can often suggest the pattern to be used. It can be observed that although there is no "smooth" pattern, there is a definite declining trend noticeable in both the graphs. To go a step further, the scatter points can be joined to indicate a rough trend, as shoxm in Figure IV-3 for the logarithmic graph. This mode of presentation is indicative of the trend, and accentuates the dispersion for unusual values. However, as a basis for extrapolating a trend, some form of smoothing would have to be undertaken. Disregarding some of the extreme deviations, it can be observed in Figure IV-1 that there is an initial decline, disrupted slightly between the tenth and the fourteenth unit, and the data flattening out between the fourteenth and the nineteenth unit. Several patterns can fit this set of data such as a straight line, a curvilinear projection indicating a fast initial decline and a steady straightening out, or even a "flow" pattern. Using the method of least squares, a linear function has been fitted to the data in Figure I\'-4. The least

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148 squares method for fitting a straight line on logarithmic grids is considerably complicated, and due to the lack of references on its application. Appendix C has been provided to illustrate the derivation of the straight line involving logarithmic computations. The data presented in Table IV-I can also be represented by a curvilinear pattern as illustrated in Figure I\^-5, where a third degree polynomial has been fitted, using the orthogonal polynomial computations. The third degree curve was used in preference to the second degree, for the second degree curve tends to rise up sharply tov7ard the end; whereas the third degree curve has one more hump, and hence illustrates the curvilinearity more forcefully. Anything more than the third degree would be inadvisable due to the limited number of units being considered. Let us suppose that the trend is to be used for forecasting purposes, in which case either the straight line or the curvilinear projection could be extended, as sho^m by the dotted lines in Figures I\''-4 and rv-5. How reliable are the exterpolated values for forecasting purposes? Other things remaining the same, both trends might indicate reliable results. However, there are so many variables influencing the production process that the ceteris paribus assumption might not be valid. As discussed later in this chapter, workers might be shifted within crews, new X'jorkers introduced, the physiological, psychological, and sociological environment might change, tooling might be altered, and engineering and design changes might be introduced, any of which can produce variations between units. Moreover, a major change may be undertaken, which can completely upset the trend. For example, a new assembly station may

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150 be started vrith a few experienced workers transferred to this new section, and other less experienced workers substituted, resulting in a disruption of the trend. Hence, the reliability of the extrapolation would be dependent on the degree to which the factors influencing experience would be affected in the future. To continue the problem at hand, production times on the next twenty-five units were ascertained, and these have been presented in Table IV-II. T-Jhen plotted on logarithmic graph paper along with the data on the first nineteen units and the expected trend using the linear projection, the graph appears as indicated in Figure IV-6 . A mere glance indicates that the estimated figures are nov;here near the actual values, for a majority of the plot points are significantly above the extrapolated line. In this case, although not presented here in graphical form., the curvilinear projection shovjn in Figure IY-5 does not prove to be any m.ore efficient than the linear representation. An interesting point to note is the impact of the quantity selected by the analyst as the num.ber of units at which a smooth projection can be statistically derived. To illustrate the implication of this rather important aspect, the labor hours for the entire forty-four units are used as the sample, and projections to fit this information sought. Figure IV-7 is a plot of the information on the entire lot of forty-four units plotted, with AB being the line of best fit for the entire sample. The straight line CD is the line of best fit, as derived previously, for the first nineteen units only. The differences in trends due to varying cut-off points for fitting curves can be visualized from

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151 TABLE IV-II Assembly-Time Analysis for the Next Twenty-Five Units Produced Unit

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154 the graph. Similar differences can also be evidenced using the polynomial approach for fitting trend lines in place of the least square method. This finding leads to a very important hypothesis which has been accepted by statisticians, but to which no mention was found by the author. To state this hypothesis: the fittin,-;; of a trend line is con siderably influenced by the size of the sample accepted for purposes of analysis . Putting it differently, not only can different trends be derived by the application of different statistical methods from the same data, but different trends may also be extracted from the same data using the same statistical tool but using different quantities for the derivation of the trend. A way out of the dilemma may be sought by using the cumulative average plots in place of the unit hours for the cumulative average values tend to be more "conservative" and less erratic than the unit hours. Figure IV-8 shows the cumulative averages, from Tables IV-I and IV-II, at the different levels of production plotted on logarithmic grids. There is little doubt that this projection indicates a more understandable trend, due to the fact that the process of averaging tends to balance off the extremes. However, once again a linear function from considering only the first nineteen units presents us a different slope, line PQ in Figure IV-8, than the projection that results from taking all forty-four units into consideration, as represented by the straight line RS in Figure IV-8. I-Jhereas PQ approximates an 86 per cent experience rate, RS is closer to a 96 per cent rate. Relatively speaking, this discrepancy

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156 can be considered as excessive. To validate this assertion, the two trends have been extended in Figure IV-9 to include values for 10,000 units. The line PQ Q' implies that the cumulative average for 10,000 units will be approximately 1,400 hours, whereas RSS' indicates the average as alm.ost 4,000 hours per unit. The difference between these two estimates am.ounts to an average of 2,600 hours per unit, which would imply a variance in the estimate of almost 26,000,000 hours for the entire production. This is truly considerable. The above discussion indicates the limitations of relying on statistically derived extrapolation, especially for forecasting longrange values. The degree of risk involved in forecasting would be proportionate to the distance of the extrapolated estim.ate from the actual trend. An estimate for a distant quantity would be much more liable to error than a short-run estimate, for greater would be the opportunity of predicting pertinent influences in the near future than in the distant future. As stated earlier, Brandt has suggested the use of arithmetic grid paper, and application of orthogonal polynomials for detecting trends. The figures represented in Table IV-I and IV-II have been replotted on arithmetic grid graph paper, as sho^^m in Figure IV-10, and the first, second, and third degree lines drax-m to indicate what they look like. This study indicates that whereas a linear fitting may be advisable for extrapolating purposes, the second and third degree polynomials vTith their resulting curvilinear trends may be profitably used for control purposes. Patterns could be observed, their fit checked.

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159 and investigations undertaken to understand the reasons for these patterns. The mechanical calculations for curve fitting can be expedited by the use of computers. Whenever computer facilities are available, not only can the necessary calculations be done quickly and efficiently, but various other information can also be collected. For example, the above problem was programmed to obtain linear fits, and along with the values of the Y intercept and the slope, the standard deviations of X and Y, the standard error of estimate, the coefficient of correlation, the coefficient of determination, the standard error of the slope, and Ttests for the slope, were obtained. These pieces of statistical information could prove very useful in the hands of a proficient statistician. As indicated earlier, procedures are available for testing the significance of the contributions of various degree functions. Such tests were made on the data used for the illustration in this section, 12 using Snedecor s approach. This approach is similar to that expounded by R. A. Fisher in his Statistical Methods for Research Workers which contains a detailed exposition of the reasoning behind the procedure 13 for testing the reliability of fitted curves. However, testing curve fits on logarithmic grids can be extremely complex and inconvenient. For this reason, it is suggested that curves fitted on arithmetic grids be first tested, and if necessary, tests can be conducted on logarithmic curves. In the case of the above example, the first degree curve appeared to be significant as a fit for both the sample of nineteen units

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160 and the larger group. Surprisingly, both the second and the third degree fits proved to have insignificant representation. An attempt is next made to "fit" linear patterns as hypothesized by the learning curve theory on the information given above. Only the set of data presented in Table IV-I has been used for purposes of simplifying the illustration, and similar fits can easily be derived for the entire lot of fortyfour units. In Figure IV-11, a linear unit hour function along with a curvilinear cumulative average function has been fitted by eye; vhereas, a linear cumulative average function along with a curvilinear unit hour line has been projected in Figure TV-ll. It can be proved statistically that these fits are not the best fits, for visual judgment has been used and trends fitted arbitrarily. However, the point is that such fits can be "derived," introducing a substantial opportunity for error. The Experience Rate and the Slone of the Experience Curve Definition of the experience rate The experience rate is usually denoted by a percentage V7hich signifies the complement of the rate of im.provement between two production quantities which bear a duplicated relationship. For example, a 70 per cent experience rate indicates that there is a 30 per cent decrease in costs or labor hours between doubled quantities. According to the experience curve "theory," this experience rate would be constant over the entire range of production for the cumulative average, unit hours, or lot averages, in accordance -VTith the "version" accepted. Hov/ever, the position taken by this study is that the rate need

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163 not be constant, for the possibility of curvilinear trends cannot be overruled. In case of curvilinear models, the rate of improvement would be different within the range covered by the doubled quantities, and, hence, it might be advisable to measure changes in smaller amounts. For the purposes of analysis, the experience rate is defined as the complement of the percentage decrease in costs or labor hours between doubled quantifies produced. In case of curvilinear models, a linear function may be approximated, or the curvilinear portion adjusted by fitting a number of linear segments, as explained further on in this section. It should be noted that relevant analysis of the experience rates does not call for extreme accuracy, but rather is concerned with rough indications. As defined above, the experience rate can be expressed by the mathematical formula R = ^^2n or R = !^ where R stands for the experience rate expressed as a percentage, CA is the cumulative average, U is the unit hours, and n is the cumulative output. For purposes of illustration, a linear cumulative average production time-quantity relationship has been presented in Figure IV-13 (a unit hour function could be used in place of the cumulative average without affecting the analysis in any manner). The function's rate of decline can be ascertained by taking any two cumulative outputs, provided there is duplication of original output involved. Thus if n is assumed to be five, 2n would be ten. Taking this as an example, the slope can be found by substituting the proper

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L65 values in the formula:

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166 TABLE IV-III Slope Coefficients, Conversion Factors, and Angles of Decline, for a Range of Experience Rates III IV Conversion Degree of Factor ' Angles .4854 27^14 .5058 26°18' .5261 25°22' .5459 24°24' .5655 23°29' .5850 22°32' .6041 21°36' .6229 20°39' .6415 19°43' .6599 18 47' .6781 17°51' .6959 16°55' .7137 ^^0^9' .7312 15n°^' .7484 14 07' .7655 '"3°12' .7824 12°17' .7991 11 22' .8155 10°27' .8319 9°27' .8480 8 39' .8639 7°45' .8796 6 52' .8953 5°59' .9108 5 06' .9260 4°14' Source: Adapted from R. B. Jordan, "Learning How to Use the Learning Curve," N .A .A .Bulletin (January, 1958), p. 30. I

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167 illustrated in Figure IV-13 has a slope of .3219, as indicated by columns 1 and 2 in Table IV-III. The exponent of the slope can also be calculated with the help of simple trigonometry. Referring again to Figure IV-13, we can take any point B on the Y axis, below the Y intercept A (which indicates the cumulative hours for unit one). From this point B, a line parallel to the X axis can be dra^i/n to cut the linear function at point C. This would then provide a right angle triangle ABC, of which AC would be the hypotenuse, BC the abscissa, and AB the ordinate. The exponent of the slope of AC could then be calculated by dividing the length of the abscissa into the length of the ordinate. Thus, g _ Ordinate = AB _ 3219 Abscissa BC Now, this relationship of ordinate to abscissa can also be expressed by the tangent of angle ACB, shovm in Figure IV-13 as angle L. The degree of angle at L could be measured, and the exponent located by looking up its tangent in any natural tangent table. Thus, for the function shoxm in Figure IV-1, angle L = Tanl7°51' = .3219. The degree of angles, corresponding to the complementary rate of decline percentages and their respective exponents have also been presented in Table IV-III. It is not necessary that the right angle triangle be located below the function. Any point, say N, can be selected above the function, and a right angle triangle formed by dropping a perpendicular to cut the function at point N, and a line parallel to the X axis dra^^m to meet the function

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168 (not necessarily at A). In this case, angle NAM would be L', AN would be the abscissa, and NM the ordinate. The exponent would be expressed as: NM S = AN = -3219 or, angle L' = 17°. 51' = .3219. In short, the same result would be obtained by utilizing the trigonometric right angle triangle, and merely measuring the angle formed by the abscissa and the hypotenuse, or dividing the length of the ordinate by the length of the abscissa. If the experience rate is kno^^m, the exponent of the slope can also be located with the help of the formula: c 2 log R log 2 For example, the exponent for the 80 per cent curve would be: 3 ^ 2 log 80 ^ 2 1.90309 ^ 0^3^,5 ^ log 2 0.30103 This formula, S = " '^ •*• , expresses mathematically the relationlog 2 ' "^ ship between the experience rate and the exponent of the slope. Can an experience rate or rates be ascertained for a curvilinear trend? A rough approximation can be utilized by fitting a first degree curve, even though such a representation does not provide the m.ost significant fit. If further accuracy is necessary, linear segments could be inserted into the curve in order to ascertain different rates within the curve. The number of such segments to be dra^m would have to depend on the degree of accuracy needed. Once the straight lines have been drav/n, their rates and slopes can be determined as indicated for linear functions.

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169 This approach could conceivably be used for all forms and models of dynamic production data. Column III in Table IV-III represents conversion factors which can be used for quick calculations of cumulative averages from unit hour figures, and vice versa. For example, the conversion factor for an 80 per cent slope is .5781. To derive the cumulative average curve given the unit hour curve, the unit hours at any point can be divided by the conversion factor to arrive at the corresponding cumulative average. Two such points can be derived, joined, and extended to arrive at the cumulative average curve, or simply a straight line parallel to the unit hour curve can be drawn using one point to indicate the distance between the lines. Similarly, any cumulative average can be multiplied by the conversion factor to arrive at its corresponding unit curves, and the curves constructed in the manner indicated above. Another m.ethod has also been suggested. If the unit hours line has been plotted, the cumulative average can be derived by calculating the distance between the top of any one vertical cycle and the conversion factor on that cycle, and a line draxi/n parallel to the unit curve indicating the distance calculated in the above fashion. To derive a unit hour line, the same distance could be marked below the cumulative average curve, and a parallel line dra\m to represent 17 the unit hour curve. Aids for mathematical calculations Several tools have been suggested as aids for mathematical calculations involved in dynamic production data analyses. Most of these aids have been originated by industrial engineers and researchers to facilitate

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170 the mechanical calculations encountered, and hence suffer from the limitations involved by the acceptance of preconceived m.odels. Most of these tools assume some form of a linear model, and hence cannot be used V7ithout a detailed investigation into their applicability. A few of the aids suggested have been discussed below. Since the logarithmic scale is usually em.ployed for dynamic data analyses, the use of slide rules for quick computations is conceivable. Rigdon has supplied a comprehensive discussion on the use of slide rules, including illustrations of special slide rules v.'hich were found to im.prove calculating efficiency. -^^ The author points out that most of the slide rules illustrated were made of plain cardboard, and proved sufficiently durable and accurate. The use of a "logarithmic square" has been suggested by W. A. Rayborg, Jr." Tnis logarithmic square is a plotting aid which can be transformed onto transparent paper or plastic and used for fast calculations of the cum.ulative average or the unit hour curve. A "computer" which can be of any size, including pocket size, has 20 been illustrated by Doris M. Eisemann. This computer consists of three sheets (of durable plastic), on V7hich the cumulative average, the unit hours, and the cumulative total curves are sketched, each on a separate sheet. These sheets are assembled so as to be able to slide over a logarithmic grid on which the transparencies can be superimposed. Once m.ore, faster, more accurate calculations have been asserted through the use of this "computer" by its originator. A more advanced mathematical treatment has been explained by Metz 71 in the form of a nomograph. It is claimed that a momograph, once con-

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171 structed, can be used to provide extremely fast, accurate and exhaustive information. Hox^ever, it is important that one understand the nomograph methodology in order to develop and use such an intricate tool. The use of electronic computers for aiding calculations has often been suggested, especially by federal agencies. For example, Sandler has illustrated the application of computer programming for audit purposes in 22 a recent article. Most of the aids mentioned can be very helpful; however, care must be taken to understand their assumptions and limitations for the danger of misuse is ever present. Significance of the Experience Rate Since the experience rate denotes the complement of the percentage decline in costs or production time with increased production, it is evident that a smaller rate implies a greater degree of improvement than a higher rate. Hence, a 60 per cent rate indicates a faster decline in costs than a 70 per cent rate; the latter implies a faster rate of decline than 15 per cent, and so on. Theoretically, it would be possible to have unit hour curves representing rates within the entire range of 1 to 100 per cent (or even more). However, the cumulative average rates would have a theoretically possible range of anything over 50 per cent to 100 per cent (or more). The reason is easy to comprehend. A 50 per cent cumulative avera.ge rate would m.ean that if the first unit were produced in 1000 hours, the second unit would have to be produced without any work — a theoretical impossibility. The practical limits would be somevjhere between 70 and 100 per cent

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172 for both the unit hours and the ctraiulative average rates. This author's experience seems to indicate that a substantial majority of products would fall within the 80 per cent to 95 per cent range. Docs a smaller experience rate or a steeper experience curve necessarily indicate a greater degree of attained efficiency for a product than a higher experience rate? Several researchers have answered this question with an unconditional affirmative; hov/ever, the research undertaken for this study seems to indicate a cautious affirmative reply to the question. It can be argued that a steeper slope indicates a higher rate of decline in production time with increased quantities, and consequently, the higher decline rate implies increased efficiency through improvement attained via the experience gained. This line of reasoning has been presented by several studies, and empirical evidence has been presented to validate the hypothesis that a higher experience rate indicated by a steeper slope in any situation implies a greater scope for experience to favorably affect improvement. It is logical to assume that where an operation is largely composed of assembly operations for which direct labor is the predominant element, there would be a greater scope for improvement than where the major portion of the manufacturing process involves a pre-set automatic machine. This hypothesis that machine progress ratios are likely to be smaller than assembly progress ratios was tested by Hirsch. Using sophisticated statistical tests, he found that in six of the seven cases tested, the machine improvement rate was significantly sm.aller than the assembly rate.

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173 Pooler has also attempted to validate his thesis that "the more an operation is made up of assembly, the greater the reduction of labor time possible." Pooler has presented a table, reproduced in this study as Table IV-IV, showing the ratio of machining time to assembly time and their corresponding experience rates for four industries. This table indicates that as machining time goes up, the rate of improvement goes down, leading to a higher experience rate. It should be noted that Pooler's analysis is neither scientific nor reliable (as he him.self indicates). However, the tendency pointed out by the table can be accepted as a fair approximation of the relationship between assembly and non-assembly type operations . A similar analysis was conducted by Morton S. Titleman who used correlation analysis to find a definite relationship between the manual ratios and experience rates. His findings have been presented in Table IV-V, which clearly indicates a lower experience rate for operations involving a higher ratio of manual-to-mechanical work. The above findings seem to validate the hypothesis that there is a higher percentage improvement in operations involving human labor, and that there is a definite relationship between improvement which reflects efficiency as evidenced by the experience rate, and the human content. Production efficiencies can be reflected on the experience rate. Since direct labor is only one aspect of the total hum.an labor involved in the process of production, it can be asserted that there is a definite relationship between the experience rate and the degree of efficiency attained as influenced by the production process, the nature of

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174 TABLE IV -IV Relationship Betv/een Manual-Mechanical Ratios and Experience Rates for Four Industries Industry Machining Time (%) Assembly Tim.e (%) Experience Rate Aircraft Engines Electrical Machinery 75 45 40 25 Source: Adapted froraV. H. Pooler. 73. TABLE IV-V Relationship Between Manual-Mechanical Ratios and Their Corresponding Experience Rates for Various Operations Operation Operation Content Experience Manual (7,) Mechanical (7,) Rate (7.) Grinding-Manual ChippingPneumatic Blast Cleaning Milling with jig Assembly — no jig Milling — no jig Welding — submerged arc Gas cutting, thick plates-machine Assembly with jig Welding — manual Gas cutting, thin plates-machine Fitting Shearing plates 10

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175 the operations involved, and the intensity of other factors affecting experience. Does this observation also imply that a smaller experience rate is necessarily "better" than a higher rate? Has a product, showing a steeper experience curve slop, been produced by more efficient means than another showing a slower rate of decline? The above question cannot be answered on a priori judgments. Detailed analysis regarding the production process and the data utilized would have to be undertaken before any judgment regarding efficiency comparisons can be made. The reason for this cautious attitude is explained below. The experience rate is influenced by two determinants; the exponent of the slope and the labor-hours at unit number onel However, there is a definite relationship between the cost or labor hours at unit one (Y intercept), and the exponent of the slope. A detailed empirical investigation undertaken by Harold Asher demonstrated that there was a marked relationship between the experience rate and the labor hours at unit one. Various other studies have also indicated the implications of pre-production planning on the time taken to produce unit number one 27 and the experience rate witnessed during the course of production. It can be logically argued that if proper pre-production planning is undertaken, including better tooling, scheduling, equipment, etc., the labor hours or the unit cost for the first completed unit is likely to be lower than without such extra care (assuming the rate of production and the estimated volume to be given in both cases). Moreover, proper planning undertaken at the initial stages would lessen the scope for

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176 improvement during the course of production and hence a flatter experience curve lying considerably lower than one with a smaller amount of pre-production planning would result. If production is started on a product without proper planning, the initial cost per finished product would be high. However, the haphazard beginning would leave considerable scope for improvement, for several "bugs" which could have been removed before production was started on the product would be discovered and removed as production continues. Hence, a higher Y intercept V7ith a lower experience rate would be the result. From the above discussion it can be deduced that a faster rate of improvement does not necessarily imply a more efficient production situation, and comparisons should be avoided as far as possible. Of course, if equal emphasis has been placed on the pre-production planning of similar products using similar production processes, a comparison might be in order. As Asher sums it up: "Any statement concerning the relative efficiency of different producers should take into account those factors that appear to influence unit number one man hours and ,.28 progress curve slope. Factors Influencing the Experience Rate It was seen in the last section that the experience rate can be affected by two sets of factors: pre-production activities and duringproduction influences. A detailed investigation into these two sets of factors has been undertaken in this section.

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177 Pre-production factors Decisions made regarding the anticipated volume of production can substantially affect the experience rate. The anticipated volume of production can have as its two components the expected rate of production and the estimated length of production, which can conceivably influence engineering and production decisions, which in turn can affect 29 the experience rate. Although a cursory glance at the implications of dynamic production data might indicate that the rate of production and the anticipated duration have no influence on the experience rate, the following discussion indicates otherwise. When a production order is received, the production planning department has to initiate all possible plans to produce the product, taking into consideration the requirements for capacity, materials, labor, supervisory personnel, tooling, etc. under the constraints of maintaining minimum costs. To be more specific, decisions regarding product design, methods, tooling, and organization have to be made, in order that the product can be produced in the most economical manner. Most of these decisions cannot be made efficiently unless all the relevant information is made available, which would include details on the anticipated rate of output and the duration of production. For example, consider the problem of tooling. The production department is usually given instructions regarding the assembly of a product. Unless the rate of output is specified, the extent of tooling cannot be planned for in any m.anner which can be considered efficient. If one unit is to be assembled every three months, the initial tooling design and other requirements would not be

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178 the same as when production of three units a month is anticipated. Similarly, completely different decisions would have to be made regarding tooling if ten units were to be produced over a period of three months instead of a hundred units over a period of thirty months. It is not difficult to verify, conceptually or empirically, that different equipment, designs, factory layouts, supervision, etc. would be needed depending upon the decision m.ade regarding the two important components of the anticipated volume of production: the expected rate of production and the estimated duration of production. Some of the factors which can influence initial cost or production time and hence affect the experience rate are listed below. (It should be noted that there can be a considerable degree of interdependence and interrelationship betX'jeen the factors, and their independence is recognized mainly for purposes of analysis.) 1. The expected volume of production, which can be influenced by the anticipated duration of the production run, and the estimated rate of output, as discussed above. 2. The type of equipment selected, including the plant capacity to be devoted to the production of the product in question. 3. The type of tooling to be used, including the selection of proper tools, and the degree of effort expended tovjard obtaining more efficient tooling to suit the needs of the expected volume and rate of production. 4. The percentage of work to be subcontracted. ^-Jhatever work is subcontracted would then be influenced by the subcontractors' experience

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179 rate for that portion of production. Thus, subcontracting a portion of work which might be new to the producer, but which has been worked upon by the subcontractor, can result in lower initial labor time and cost, but a different experience rate. 5. A similar argument can be supplied for the selection of raw material suppliers. 6. The extent to which detailed engineering specifications are utilized. A higher degree of engineering effort can lead to a slower rate of decline for the experience rate during production. 7. Connected to the above is the magnitude of the effort expended on settling problems regarding manufacturing design, inspection tests, etc. 8. Also related to the two preceding factors is the extent of coordination considered between the product design and production engineering before manufacture of the product is initiated. 9. The importance of proper work-methods planning needs to be recognized. An initially well-planned flow of men, material, machinery, and the product-route can considerably influence the experience rate in the course of production. 10. Connected with the above is the factor of shop organization, including materials handling, pre-production training, skill, etc. 11. The implications of experience gained in similar products can also be utilized for affecting the rate. Thus, transferring workers from one operation to other similar operations can result in a lower but flatter curve than starting a fresh group on the job.

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180 12. The extent of recognition given to the relationship between the difficulty of the task and the ability of the organization to perform it has been suggested by Conway and Schultz as yet another pre30 production factor. 13. The availability of adequate materials and component parts can also be planned for in advance, or improved upon in the course of production. 14. The planning and acquisition of proper personnel is another factor. 15. The impact of expenditures on research and developm.ent needs little explanation. 16. Finally, Crawford and Strauss mention factors such as the relative priority given to a product, efficiency of operating controls, frequency of schedule changes, and the degree of pressure attached to the program, as dictating the initial cost of production and the result31 ing during-production experience rate. During-production factors Once pre-production planning is completed and the product put into production, the process of further improvement starts. In spite of considerable care taken at the pre-production stage, there are bound to be coordination errors and peculiarities which can be improved upon in the process of production. Thus, tooling can be bettered, engineering updated, production methods and scheduling improved, and better coordination achieved as the particular deficiencies are evidenced. Above all, the factor of human labor being introduced presents opportunities for

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181 learning and improvement with increased production. Several of the pre-production factors, mentioned earlier, affecting the initial cost of the product and hence the experience rate, also affect improvement during production, although in a different manner. Factors such as tooling, engineering, etc. » which affect the initial cost can be improved as production continues and hence can affect the rate as during-production factors also. An im.portant difference between pre-production planning and during-production factors is that, in the first case, the effect of the factor is of a once-and-f or-all type, but one that could lead to a major change. On the other hand, the duringproduction factors are continuously affecting production time and costs, and lead to relatively minor changes. Hence, the nature of their effect on improvement is of a different intensity and character. 32 Some of the during-production factors are listed below. 1. Individual workers' learning or improvement . Although opinion is divided regarding the relative importance of this factor as a determinant of the experience rate, agreement is unanimous on the fact that experience gained by the workers through repeating similar operations does lead to a decline in labor hours as production progresses. For example, Hirsch seems to emphasize the individual worker's learning as 33 the principal factor leading to improvement. Several other studies also indicate, directly or indirectly, the importance of the direct laborer's potential for improvement. As opposed to this contention, other \\nriters indicate that although worker-learning is a causal factor, it is not the principal determinant of the rate of improvement. For

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182 example, a study undertaken at the Boeing Aircraft Company labels the additional skills gained by direct workers as "a small factor." A similar position has been taken by Conway and Schultz, who assert that "operator learning in the true sense of performance of a fixed task is 35 of negligible importance in most manufacturing progress." The findings of this study indicate that the degree of importance of worker learning depends upon the particular conditions surrounding the production process. It can be argued logically, and verified empirically, that human beings do improve through repeating an operation, and this human learning can affect performance. However, the degree of importance placed on this factor cannot be determined a priori. Blume and Peitzke point out that through repetition the operator decreases time spent on analyzing operations before starting the work, his physical motions become more efficient, and rejections and reworks 37 decrease. To these factors can be added better coordination between the mental and physical requirements for the job, and improved psychological factors such as confidence, or application of initiative once the mind has opportunity to lay aside the conscious direction of mechanical acts. That is, experimentation aided by the human mental capacity leads to an improvement on the part of the workers. Fowlkes indicates the importance of "familiarity" as a major reason for worker improvement. Thus, familiarity with the task, tooling, engineering and planning papers, inspection requirements, associated operations or installations, and manufacturing or assembly techniques involved, can be considered as elements leading to individual worker's learning or

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183 improvement. Along with this factor of familiarity are other influences such as improvement in morale, supervision, layout, and manufacturing aids. It should be pointed out that the reasons for learning evidenced in individuals is beyond the scope of this study, for the question can be more competently analyzed by one proficient in the study of psychology. It is restated that a producer can profit considerably by initiating an interdisciplinary study to research the impact of worker learning on costs and labor hours, and to ascertain means for improving the learning process under the given environment.' An observation m.ade in the course of this study was that although the existence of workerlearning at the initial stages of production can be validated, whether the rate of learning can be sustained at all levels of production has not been validated. Can the workers improve at the same rate after a thousand units have been produced, or would monotony and boredom actually deter further improvement? Is there a limit beyond which one cannot expect further improvement? These questions cannot be answered except by introducing value judgments. "Evidence" to support either contention has been supplied by authors, however, and unless detailed research can be undertaken to validate the hypothesis that the rate of improvement continues to infinity, one can merely hope that Hirschmann's assertion in favor of limitless improvement is sounder that the 38 opposite contention. 2. Improvement in tooling . The importance of proper tooling was discussed in the section on pre-production factors. The degree of im-

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18A provement in tooling in the course of production would have to depend considerably on the pre-production planning for tools. Greater the effort expended on acquiring tools before production commences, fewer the opportunities for improvement after production is started, and vice versa. As minor variations in design, components, and methods arc introduced, the available tooling might have to be adjusted and adapted for increased efficiency. The numerous design changes that are initiated, along with the need for specific tools which aid individual workers or crews, necessitate frequent tooling changes. Once again Fowlkes is referred to for details regarding the elements contributing to improved tooling. His list includes correction of tooling, engineering or lofting effors, improvement of tool design, simplification of tool usage, refinement of manufacturing breakdown and operation sequencing, incorporation of changes, development of new tooling techniques, acquisition of m.odern machine tools, expansion of gauge and template coverage, and, finally, determination and m.anufacturing of required duplicate tooling. 3 . Improvement in supervision and inspection. Improved supervision through task familiarity could encourage progress, increase effectiveness, minimize delays, and decrease idle time. There is considerable scope for im.provement in the area of inspection. More efficient inspection procedures can be initiated, such as inspecting at different stages, developing more efficient controls, introducing proper feedback systems, aiding the production department in the minimization of rejects and reworks, etc. 4 . Improvemc': on the part of higher management . Management

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185 policies play an important part in the determination of the experience rate. As Thue points out: Decisions of management in regard to labor relations, working conditions, investment in inventories, introduction of new machines and processes, and many other topics have a profound effect on the time reduction record. . . , General management policy will affect the level of the time reduction curve, while a change in management policy will affect the slope of the curve.-"" To take an example, improved worker-management relations can affect the general morale, leading to a more conscious effort on the part of the workers. Also, use of properly motivated employee suggestion schemes, cost accounting proposals, or decisions regarding wage incentive schemes can affect the experience rate noticeably. Moreover, with the passage of time, more refined and advanced management tools for planning and control are being introduced to increase management efficiency. Thus, refined statistical tools such as linear programming and inventory control procedures can lead to fewer stoppages, more efficient scheduling, etc. However, for these statistical tools to be effective, reliable data have to be furnished, and the reliability of any information can be accepted only after careful study and constant checking of the raw data, which can be improved as production progresses. There is considerable scope for management to improve its planning, organizing, staffing, direction, and control with increased production and the lapse of time. 5. Improved clerical, administrative, and personnel services . This factor is more or less an offshoot of the one discussed previously and, hence, no attempt at further elaboration is made here.

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186 6. Engineering and design modifications . As production increases, there is scope for initiating engineering and design changes which can allow minor economies to be experienced. These improvements can arise due to design simplification, establishment of design fixes, normal development of new techniques, classification of drawings, and correction of engineering and lofting errors, as pointed out by Fowlkes. 7. Im.provement in production methods and processes . With continuing production, there can be improvement through better operation sequences, and increases in machine feeds and speeds. More efficient manufacturing methods may be utilized to facilitate a smooth flov? and to minimize the chances of production breakdovms. Better shop organization can be undertaken to avoid lack of balance and congestion, and to facilitate job assignments and scheduling of shop loads. Work can be released in more economically sized batches as production requirements are better knoT-Tn. Thus, as Fowlkes indicates, improvement in dispatching and shop loading, refinement of manufacturing and assem.bly scheduling, familiarity with routing and usage, and correction of erroneous paper work can lead to improvement in production control. 8. Industrial engineering improvements . This is another area commented on by Fowlkes, who asserts that the development of manufacturing aids, optimum sequencing of installations, and other industrial engineering methods such as time and motion study, m.ethods analysis and improvement, value engineering, cost reduction programs, and systems and procedures im.provement, can affect the experience rate. Improvem.ent in machinery and plant layout needs special m.ention, for m.aterial handling provides

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187 excellent opportunities for during-pr eduction improvement. 9. Improvement through more efficient combination of resources . The use of hand labor as contrasted to utilization of machinery can be better adjusted as production continues. Thus, it might be found advisable to use special machinery to aid an operation which was initially performed by labor. Furthermore, additional capital equipment may be utilized, or portions of the product may be sub-contracted. The assembly-tim.e to machinetime ratio may be adjusted to suit production requirements, thus affecting the experience rate. 10. Improvement in materials . The procurement of materials, including the quantity and the quality of the materials to be used, can be improved. Better quality can lead to less breakages, rejections, and reworks. Initial production would indicate the acceptability of materials used, and changes could be made to suit the particular requirements. Thus, improved sources of ma-terial supply for quality, quantity, and delivery, normal research and developm.ent of improved material and material supply sources, and more efficient procurement of forgings and castings, proper gauges and shapes, and optimum sized materials to minimize cutting and scrap, are some of the elem.ents referred to by Fowlkes as aids to material improvement. 11. Improvement in the state of knowledge . No business entity is completely detached from developments experienced by others, and improvements witnessed in other similar production situations are bound to be shifted over in the course of manufacturing. Thus, external forces might contribute toward more efficient means of production, for the rate of ad-

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188 vancement in technical knowledge cannot be considered as unimportant. The increase in the nuir.ber of technical and other journals, advancement of short seninar-type courses, introduction of recently-graduated workers, better inter-company relations, centralized industrial guidance, wider use of pre-progrsT-ned computer-type equipment, etc. tend to inject knowledge in the process of production that can influence a product's experience rate. 12. Improved coordination and communications . Business firms are, after all, organic systems which learn to function better with time and practice. Every system needs time to coordinate and work sm.oothly its different parts. No amount of care and scientific knowledge can cause a system, as intricate as the business organization, to function at optimum efficiency at its inception. The problem of optimum efficiency in communications is of the same nature. Thus, with the advent of production, a steady flow of improvement in coordination and communications is conceivable. As Thue indicates, "Experience provides for the development of smooth team work among workers, better coordination among supervisors, and development of smoothly operating channels of communication and .40 standardized procedures.

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189 FOOTNOTES Chapter IV 1. F. E. Croxton and D. J. Cowden. Applied General Statistics (Second Edition; Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1955), pp. 8A2-843; John Neter and William Wasserman, Fundamental Statistics for Business and Economics (Third Edition; Boston: Allyn and Bacon, Inc., 1966), p. 738. 2. Croxton and Cowden, op. cit ., pp. 216-262. 3. Neter and Wasserm.an, op. cit ., p. 520. 4. This study is greatly indebted to Dr. A. E. Brandt (retired Statistician and Head, Statistical Section, Agricultural Experim.cnt Station, University of Florida, and presently acting as statistical consultant to the College of Business Administration, University of Florida), for the extensive guidance and aid offered in the understanding and application of the statistical processes. 5. George W. Snedecor^ Statistical Methods (Fifth Edition; Ames, Iowa: The loxra State University Press, 1956), Chapter XV. 6. Ronald A. Fisher, Statistical Methods for Research Workers (Thirteenth Edition; New York: Hafner Publishing Company, Inc., 1958), Chapter VIII. 7. Brandt, "Some Notes on Some Growth Functions," unpublished paper written for the Health and Safety Laboratory, U. S .Atomic Energy Commission, New York Operations Office, n.d., p. 30. 8. The terms power curve, exponential curve, and logarithmic curve have been used here, as defined by Allen E. Edwards, Statistical Methods for the Behavioral Sciences (New York: Holt, Rinehart and Winston, 1964), pp. 129-138. 9. Croxton and Cowden, op. cit ., pp. 265-266. 10. A detailed exposition of the method has been presented by Snedecor, op. cit .. Chapter XV. 11. In the course of personal interviews. 12. Snedecor, op. cit ., Chapter XV. 13. Fisher, op. cit .. Chapters IV and VIII. 14. H. Asher, Cost-Quantity Relationships in the Airframe Indus try (Santa Monica, California: The Rand Corporation, July 2, 1936), p. 16.

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190 15. A. E. Burrow, "Use of Learning Curves in Contract Audits," The GAP Review (Winter, 1957), p. 33. 16. B. T. Sanders and G. E. Blystone, "The Progress Curve--An Aid to Decision Making," N.A.A. Bulletin , XLII (July, 1961, 85. 17. A. W. Morgan, "Experience Curves Applicable to the Aircraft Industry," The Glenn L. Martin Company, Baltimore, Maryland, September 27, 1957, p. 6. 18. C.J. Rigdon, "Analysis of Progress Trends in Aircraft Production," Aero Digest , XLV (May 15, 1944), 132-37. 19. W. A. Rayborg, Jr., "Mechanics of the Learning Curve," Aero Digest , XLV (November, 1952), 17-21. 20. D. M. Eisemann, "The Progress-Curve Computer," Operations Research , VII (January-February, 1959), 128-130. 21. P. B. Metz, "A Manufacturing Progress Function Nom.ograph," The Journal of Industrial Engineering , XIII (July-August, 1952), 253-256. 22. I. J. Sandler, "Dial for Computer Audit Assistance," The Federal Accountant , XVI (Fall, 1966), 14-15. 23. W. Z. Hirsch, "Progress Functions of Machine Tool Manufacturing," Econometrica , XX (January, 1952), 81-82. 24. V. H. Pooler, Jr., "How to Use the Learning Curve," Purchas ing LI (July 17, 1961), 72. 25. M. S. Titleman, "Learning Curves--Key to Better Labor Estimates," Production Engineering , XXVIII (November 18, 1957), 37. 26. Asher, op. cit ., pp. 76-78. 27. A rather detailed investigation was undertaken by K. F. Hammer, and the results of his study have been presented in "An Analytical Study of 'Learning Curves' As a Means of Relating Labor Requirements to Production Quantities" (unpublished thesis, Cornell University, September, 1954). Mention of the subject has also been made by Conway and Schultz, "The Manufacturing Progress Function," The Journal of Industrial Engineering , X (January-February, 1959), 39-54; and E. 0. Weining, "Improvement Curve Study," Boeing Airplane Company, Wichita, Kansas, August 11, 1949. 28. Asher, op. cit ., p. 85. 29. Conx'jay and Schultz, op. cit ., p. 85.

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191 30. Ibid., p. 42. 31. As reported by M. A. Reguero, An Economic Study of the Mili tary Airframe Industry , Air Material Command, Wright-PattersD n Air For ce Base, Ohio, October, 1957, pp. 225-226. 32. An excellent summary of during-production factors has been presented by T. W. Fowlkes, "Aircraft Cost Curves: Derivation, Analysis Projection," General Dynamics, Fort Worth, CRA-64-1, August, 1963 (re-issue), pp. 15-17. This study has used Fowlkes' summarization of the "elements contributing to cost reduction" as a bench mark, with further credit given to the author in the text, wherever necessary. 33. W. Z. Hirsch, "Manufacturing Progress Functions," The Re view of Economics and Statistics , XXXIV (May, 1952), 143-155. 34. Weining, op. cit ., p. 7. 35. Conway and Schultz, op. cit ., p. 42. 36. To mention just one, R. M. Barnes, J. B. Perkins, J. M. Juran, "A Study of the Effects of Practice on the Elements of a Factory Operation," University of Iowa Studies in Engineering , Bulletin 22 (November, 1940), pp. 3-86. 37. E.J. Blume and D. Peitzke, "Purchasing with the Learning Curve," North American Aviation, Inc., August, 1953, p. 3. 38. W. B. Hirschmann, "Profit from the Learning Curve," Harvard Business Review , XLII (January-February, 1964), 125-139. 39. H. W. Thue, "Time Reduction Curves," Proceedings of the Fifth Annual Industrial Engineering Institute , University of California 1953, pp. 27-30. 40. Ibid ., p. 30.

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193 variable costing and breakeven analysis have been considered. Implications for planning, including budgeting, capital budgeting, forecasting labor and capacity requirements, production scheduling, pricing, setting wage incentive schemes, and deciding between various alternatives, arc the subjects of the section after that. The effect of experience on production time control procedures on standard costing and variance analysis, and on measuring the effects of design changes is the main topic considered under the section dealing with implications for control. A note on the potential usage of dynamic analysis for other control measures concludes the chapter. Implications for Costing The effect of experience on the total cost of a product has been implied all through tho study. In this section, further investigation is undertaken to detect its effects on the elements that constitute and affect total cost. What determines the cost of a product to the firm producing it? The generalized answer, from a cost accountant's point of view, would be" the cost of direct materials, direct labor, and manufacturing overhead, along with apportioned amounts of selling and administrative expenses. In other words, the prime cost of directly identifiable materials and labor, directly allocable overhead, a portion of general manufacturing overhead applied by means of a representative rate, a portion of selling and distribution expenses, and a portion of general administrative expenses, the latter two also being applied by means of representative rates. The means to be used for burdening the products mth

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CHAPTER V SPECIFIC IMPLICATIONS FOR MANAGERIAL ACCOUNTING The Purpose and Organization of the Chapter Having investigated the derivation, potential applicability, and other general implications of the experience factor, it is necessary that some specific effects be noted. This chapter undertakes the charge of indicating such effects inasmuch as they affect managerial accounting. The chapter has been broken up into three sections for convenience in the process of analyses, and not because the topics fall "naturally" into the three categories. The three sections are interrelated and often difficult to differentiate; however, an arbitrary compartmentalization has been undertaken to expediate analysis. Thus, standard costing can be considered under the section on costing, planning, or control, but it has been analyzed under control, for its relevancy in that area is considered more important than in the other two. It is recognized that a better analysis might result from using the traditional management functionalization of planning, organizing, decisionmaking, staffing, direction, control, etc. However, since the present study is concerned \
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194 cost of selling end administrative expenses are varied and controversial. However, they are considered as part of the expenses which, directly or indirectly affect the product cost and selling price, and hence need comment. A short note on each of these elements follows. Direct materials Does the experience factor affect the cost of materials? To answer this question one has to determine what constitutes the cost of materials. Material cost embodied in a product is m.ade up of certain quantities of raw material, times the price at which the materials were purchased. Hence, total material cost could be influenced by the quantity of raw material used, the varities of components involved, the quality of the materials, and the price at which these ingredients v/ere acquired. With increased production, all these factors can be affected. As experience is gained, the quantity of raw m.aterials used per finished product will decline. For example, it night be necessary to use a thousand units of part A to produce 700 units of finished product X in the initial stages of production. After a few hundred units have been produced, it might be necessary to issue only 800 units of A to get 700 finished units of X because familiarity with the production process might lead to less waste, spoilage, and scrap, and more efficient usage of raw materials. Also, certain components m.ay be found unnecessary or replaceable by cheaper varieties. The field of value engineering is an excellent example of an attempt toward eliminating and replacing costly components.

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195 Better matched parts can also be developed to increase productive efficiency and to decrease production time and costs. The quality of the material can also be tested and improved under actual manufacturing conditions. Poor quality material may be replaced, leading to less breakage and spoilage in the course of production. As most businessmen know, the cheapest is not usually the ideal for a few extra dollars on quality material can lead to substantial savings from the avoidance of breakage, work stoppage, loss of custom.er good will, and other profit reducing disturbances. Increase in quantity can also affect the price of the raw materials purchased. A comm.on example of savings through higher levels of production is that of quantity discounts and other possible econom.ies of large scale purchasing. For example, the raw material used in a manufacturing process may be the finished product of som.e other firm. If so, materials, labor, and overhead would have been expended by this original producer to get the product into its finished stage. If these elements are susceptible to improvement, as they very well could be, then with increased production the price of the raw materials can be affected. In his famous article, T. P. Wright commented on the implications of experience on the cost of materials.^ Wright distinguished between "raw" material and "purchased" material, and although the distinction has not been clearly explained, his reasoning is apparent. His point seems to be that material cost per unit of product does decline with increased production, and the rate of decline is dependent on the degree to which the vendor's production process is influenced by increased

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196 production. Thus, the raw material cost curve would be flatter than a purchased material curve, for the latter involves a greater degree of labor in the vendor's production as compared to raw material. It should be noted that the lower cost of materials may be offset by the higher prices from inflationary trends affecting the value of the monetary unit. If possible, special indices to counteract the effect of inflation should be used to note the effect of increased production on material cost. Miether such detail m.ight prove advantageous or not would have to depend upon the particular circumstances. Asher is of the opinion that the experience curve for m.aterials would be flatter than the direct labor curve, and is more likely to level off than the curve for labor, and feels that is more likely to turn convex, especially at large cumulative outputs. ^ The research undertaken by this study indicates a definite need for empirical investigation into the material cost implications before any warranted assertions can be made. Continuous production could conceivably affect statistical calculations commonly used for material control. For example, the minimTom order point is, in its simplest form, determined by the lead period (the time required to replenish an item) and the estimated usage of the material during the period. This estimated usage could be affected by the factor of experience, for with increased production, more units might be produced in the course of the lead period than expected under the conventional accounting calculations. On the other hand, with greater experience there may be less waste; and hence, fewer units of raw materials needed per unit of finished product. As Wilkerson points out in reference to governm.ent contracting:

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197 The contractor is often able to use the learning curve to schedule deliveries from suppliers so as to minimize storage, handling, and obsolescence costs by limiting the size of inventory to that required to sustain operations. The effect on these variables would be felt more strongly in the initial stages of production, rather than at higher levels. Once more the degree to which recognition should be given to such factors cannot be determined a priori. A distinct effect can be noted on the economic lot size for manufacture. Under conventional costing procedures, the economic lot size is determined by weighing the clerical and machine set-up costs against the cost of carrying excess inventory. However, the reduction in cost per unit with continuation of the lot production is not taken into consideration; and yet, such reduction can be used to offset the cost of carrying 4 excess inventory, as illustrated by Keachie and Fontana, With the use of calculus, the authors indicate that the effect of experience can be incorporated as a variable for calcula.ting the optimum economic lot size, and the results obtained from the use of their additional variable are definitely more reliable than those obtained from use of the conventional form.ula. It appears that this refinement might be well worth the effort expended for quantifying and utilizing the experience factor. Direct labor The im.pact of experience on labor costs needs little comm.ent for the subject has been dealt with in considerable detail all through this study. It has been noted that efficiency can be improved through repetition, and this proposition can be and has been validated in the last

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19? few decades. However, the significance of the factor would have to depend on the scope for improvement, which is dependent on the proportion of human skill and judgment involved in any production situation. Hence the scope for improvement through continuous production is definitely more determinable in connection \
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199 as the direct labor element would be. However, if machine hours or some other base is used, the effect would be more indirect and less determinate, but would still lead to a smaller amount of overhead applied per unit with increased production, given a long enough period. Turning one's attention to the actual rather than the applied overhead, it can be argued that the same forces that affect direct material and labor cost would also affect overhead cost. To illustrate with the help of a few examples, indirect material and indirect labor would react in a manner similar to that indicated for their direct counterparts, although the degree of the effects may vary. Supervision cost may be fixed for a period, but X'7ith m.ore units being produced than anticipated (without considering the experience factor), the overhead cost of supervision per unit would decline. Similar arguments may be presented for costs such as rent, depreciation, and other charges of a fixed nature. Expenditures for repairs and maintenance may be reduced with workers obtaining familiarity x^ith the production processes. Utilities m.ay be more economically utili2ed; for exam.ple, less water may be wasted, electric power turned off when found unnecessary, less fuel consumed, etc. In short, it is conceivable that increased efficiency could lead to a decline in overhead cost per unit; and this hypothesis is by no means a new one, for most cost accountants accepted its validity a long time ago. However, no research has been conducted to study the relationship between continuous production and overhead costs. Attempts in this direction were made by Asher, who did not arrive at any useful conclusions due to the difficulties encountered in the course of his investi-

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200 gation. The results of this study indicate that research into the area can prove very profitable, especially for providing information to aid overhead budgeting and control, information which is presently lacking. Total m.anufacturing cost Since direct materials, direct labor, and manufacturing overhead are elem.ents that make up total manufacturing costs, it can be hypothesized that production cost per unit would be declining with increased production of a repetitions nature. However, since each of these elements is likely to have a different rate of decline in costs with increased production, the resultant total cost function is m^ore likely to be convex to the point of origin than to be linear, as pointed out in Chapter II. The degree of convexity would then be dependent upon the proportion of these elements contributing to total cost, and the opportunities for improvement available to each of these elements. Selling and distribution expenses There does not appear to be any study which has observed the effect of experience on marketing costs; and yet, a little investigation undertaken by this study indicates a tremendous scope for fruitful investigation in this direction. Distribution costs may be classified into a few functional areas for purposes of analysis: selling expenses, storage, promotional packing, delivery, and general administrative expenses pertaining to the selling function. In each of these functions, the experience factor can be utilized for planning and control. For example, while setting salesmen's quotas, it might be advisable

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201 to determine the amount of experience each salesman has acquired. Thus, a beginner should not be pitted against an experienced salesman. True, salesmen's experience is usually taken into consideration when setting quotas, but for the most part rule of thumb methods are used. By plotting sales achieved against the time a salesman has worked might suggest some kind of trend which could be utilized for control purposes. Packing or order-filling offers considerable scope for improvement for here the proportion of human skill and judgment needed is relatively high. Forecasting requirements for material and labor needed for this function could certainly benefit from, a recognition of the experience factor. Selection and retention of personnel for these functions could be based on observing their learning patterns through individual charts. For example, Glen Ghormley, and also Knowles and Bell, demonstrate the use of charts for retaining more efficient personnel. Later in this chapter an exam.ple has been presented which indicates that even though xvorkers may require widely varied times for production of the first unit, the worker taking the higher time for such unit may prove more proficient in the long run than one who appeared to be the more efficient at the start. To state it briefly, different workers have different capacities for improvement, and only some form of quantity analysis can indicate the superiority of one employee over another. Wastage, spoilage, and breakage are also factors that can be improved in the packaging section. The cost of delivery can also be controlled considerably. The degree to which the factor of experience can affect delivery costs is dependent on the pre-delivery planning, for example, with well-planned

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202 routes the scope for improvement would be smaller than a haphazard system of delivery. However, transportation costs can be reduced by finding better alternatives, studying the sales requirements, and making the best of discounts--the finer points of distribution know-how, Xv'hich can be gained mainly through trial-and-error procedures. The potential for experience affecting sales promotional expenditures, storage, and other forms of selling expenses, does not appear to be significant. However, research would have to be undertaken in order to substantiate the tentative hypothesis, for a priori generalizations of this nature are always open to criticism. General and administrative expense Since the impact of experience on administrative costs cannot be analyzed on a per unit basis, analysis, if any, would have to be of a different nature, for this element of cost. To phrase it another way, improvement in costs due to continuous production would not influence administrative costs except in a very indirect manner. For this reason, the effect of experience can be determined only for specific operations of a repetitive nature such as billing, vouchering, typing, and clerical tasks which would not be affected by increased continuous production. Hence, investigation into such costs would have to be of the conventional cost reduction program type which is beyond the scope of this study. Cost and profit per unit The elements of cost discussed thus far, namely direct material, direct labor, manufacturing overhead, distribution costs, and general

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203 administrative expenses, were analyzed in terms of their identifiable classifications using a generalized approach. However, the question of the procedure to be used for burdening these costs on the individual product units has not been considered. Nevertheless, it is interesting to note the effect of increased quantitities on the cost per unit and the resulting profit. How can one find the cost of a product under conventional costing procedures? There are two possible approaches, with several variations for either alternative. One method for determining cost is to calculate the cost of each element involved in a product without giving consideration to the effect of quantities on production. Thus, a product can be dissected to find the material content embodied in the product, the price for each component ascertained, and material cost per unit derived. Similarly, the amount of labor needed to produce one unit, times the rate at which that labor would be remunerated, can provide the unit labor cost. Overhead can then be applied, along with selling expenses and the like. Aggregating these different elements of cost gives a cost per unit. Multiplying this cost per unit times anticipated number of units to be produced provides the total cost of production for a lot. Another approach would be to take the quantity into consideration, determine the aggregate cost to produce a lot, and divide this aggregate by the anticipated number of units to determine the cost per unit. Under conventional accounting procedures it is assumed that both these methods would provide the same result. However,, there is an implied assumption under the first method regarding a uniform cost per unit

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204 over the entire range of production. That is, the cost to be incurred for the first unit is expected to be the same as that which would be incurred for the thousandth unit, or any other unit. There is no such assumption involved under the second method, for a form of average is utilized. It is evident from the discussion so far that the assumption involved under the first method is of doubtful validity for if continuous production can lead to a decline in costs, the cost per unit would be changing as production is increased. Hence, if the cost of the product is calculated using method one, a higher cost per unit would result than if the other mode of calculation were accepted. This higher cost per unit can affect the pricing policy and the competitive position of the firm. It is much more difficult to forecast a total cost for the entire production, for this xrould necessitate a reliable estimate of the quantity to be produced, which, in turn, would necessitate the availability of means by which the costs could be accurately predicted. It is apparent that consideration of the experience factor could enhance the reliability of conventional procedures used in the process of forecasting. If prices are set by taking the anticipated quantities into consideration and arriving at some form of an average, the resulting profit may not be positive throughout the entire range of production. As a matter of fact, several units may have to be produced and delivered before any income can be recognized. Table V-I indicates a hypothetical situation where a selling price has been set, and the impact of declining cost can be noticed on the excess of revenues over expenses, assuming

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205 TABLE V-I The Effect of Declining Cost Per Unit on Resultant Profit Unit

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206 that the total cost per unit includes all expenses. It can be seen that a profit per unit is realized from the fourth unit on; ho\^ever, the company really starts earning after seven units have been sold. If this hypothetical company had ascertained its cost without considering the anticipated quantity, and priced the product at $110, it would have started off with a profit from selling its very first unit. Hov7ever, it would have suffered considerably in a competitive situation, and might conceivably have been forced out of the market. Forecasting and evaluating inventory In production situations, especially where complicated and valuable units are produced, or X\^here progress payments are involved, the forecasting of work in process inventories could prove to be a crucial calculation for the managerial accountant. Ronald Brenneck points out that one of the m.ain considerations in bidding for military or other contracts is whether the company can finance the work in process required to 8 meet the delivery schedules. To make a proper estimate of the work-in-process requirements for future periods an accurate forecast of direct labor hours per month has to be obtained. For the forecast to be reliable, proper recognition has to be given to the influence of quantity on production time. The cost and the price per unit can be calculated using the aggregative approach considering the quantity to be produced, and average cost per unit for each element obtained. The direct labor hours to be applied each month, taking into consideration the experience factor, times the calculated cost per hour, would provide the labor and overhead costs. Some means of

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207 applying material cost can be obtained to give the total cost of production per month. The cost of goods sold can be obtained by multiplying the units scheduled for completion by the total cost per unit, as calculated above. The total work in process less the cost of goods sold gives the month's contribution to inventory in process. Accumulating the total inventory in process over a period of months would provide the inventory requirement at the end of any period. This information can be extremely important for making decisions regarding the financing of operations, and the fact that the impact of experience has been taken into consideration improves the reliability of the figures considerably. In addition to forecasting future inventory needs, there might be the problem of calculating actual inventories in process. One way to do this is to make a physical count of raw material, work in process, and finished goods inventories, and price these physical amounts to arrive at their dollar values. The raw material inventory values can be determined in the conventional manner, using the pricing assumption of Fifo, Lifo, average, and so forth. Very seldom is attention given to the valuation of work-in-process inventories, except under process costing, where the assumption of flow of costs is taken into consideration. Hoxvever, under the job-order system, the cost per unit is taken to be constant for finished goods and work-in-process inventories. Whenever the procedure is to calculate workin-process inventories by ascertaining the total xrork in process and deducting the cost of goods sold (arrived at by multiplying the number of units completed times the cost per unit), the resulting inventory figure might prove inaccurate, for, as has been seen, the cost per unit may not

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208 be constant due to the implications of experience. Might it not be possible to use some form of a more accurate calculation? It appears that such a possibility does exist, for if units produced later require less time than those produced earlier, the units in process which represent different costs may be costed at their varying prices, in conformity with the actual costs. It seems advisable to illustrate the implication with the help of an example, hence a hypothetical situation with exaggerated figures has been used. The cost per unit, taking a certain quantity to be produced into consideration, for hypothetical product X, is as follows: Direct material $1,000 Direct labor (500 hours at $3.00 per hour) 1,500 Overhead (100 per cent of d. 1. cost) 1,500 Manufacturing cost per unit $4,000 Let us suppose that the inventory value is to be calculated after ten units have been produced, and the actual costs incurred for production have been ascertained at $50,000. The work-in-progress inventory may then be calculated as : Total costs incurred $50,000 Cost of goods manufactured (10 units X $4,000 per unit) 40,000 Work-in-process inventory $10,000 However, if the unit costs were estimated taking an anticipated quantity of, say, fifty units to be produced, the actual hours taken might be more than 5,000 (500 hours per unit times 10 units), for the 500 hours per unit is an average for the fifty units anticipated. Now, if it is ascertained that the actual time taken for the production achieved were 6,500 labor hours, and the material cost and labor rate were as antici-

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209 pated, the calculation for work-in-process inventory would then be: Total costs incurred $50,000 Cost of goods manufactured Materials ($1,000 X 10 units) $10,000 Labor (6500 hours X $3.00 per hour) 19,500 Overhead (100 per cent of d.l. cost) 19,500 Total cost 49,000 Workin-proc ess inventory $ 1,000 Thus, a different figure results from taking into consideration the effect of quantity for costing purposes where the factor of experience is involved. However, the Lifo and Fifo assumptions can also be used if the total costs can be broken doTvn into the cost of beginning inventory and costs added during the particular period. The point is that more accurate figures can be arrived at by using the actual costs in place of pre-determined cost per unit figures incorporating the averaging concept. Similar analysis could be m.ade for calculating finished goods inventory. In the case of process costing, it might be fruitful to note the effect of continuous production on the cost per unit over a period of time. If the influence of price level changes can be segregated for purposes of analysis, a form of evaluation for the production process can be initiated for better managerial control. In most of the discussion so far, only completed units have been assumed for analysis purposes. However, the concept of equivalent units could conceivably be adapted for partially completed units. For example, Vincent J. Shroad, Jr. has illustrated the applicability of the equivalent units concept to dynamic data analysis. The calculation of equivalent units can be undertaken using the conventional cost accounting approach, and hence no attempt has been made here to illustrate its

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210 applicability. The point to be noted is that equivalent units can be used in place of completed cumulative production for purposes of analysis. The fixed cost-variable cost dichotomy A commonly used classification for accounting analysis is the break.do^'rti of costs into their fixed and variable components. Fixed costs are defined as those costs X'7hich do not vary in aggregate with the level of production, and hence the fixed cost per unit would vary with every additional unit produced. On the other hand, variable costs tend to increase in total with each unit produced, but the variable cost per unit tends to be constant. These definitions are commonly accepted and used for break-even analysis, variable or direct cost accounting procedures, and miscellaneous decision-making computations. To state an authority on the subject: "In accounting measurements. variable cost per unit is usually considered to be constant over the 10 relevant volume range." The "relevant" range is not defined, and for all practical purposes the assumption seems to apply to the entire range of production. It is this implication regarding a constant variable cost per unit which is found objectionable, and the reasoning behind this objection is explained below. An important hypothesis implied by this study is that the variable cost per unit does not remain constant over any considerable range of production. As long as continuous production takes place, improvement would lead to a decline in the variable cost per unit. This hypothesis has far-reaching implications.

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211 Considering break-even analysis first, it is at once noticed that the calculations for the break-even point would be considerablyaffected. In its simplest form, the break-even point is calculated by the use of the formula: B.E.P.^ = ~— or B.E.P. = '^^ '$ VC "• • -u SP^ VC^ 1-SP where FC represents the total fixed cost, VC is the variable cost, and SP is the selling price, B.E.P..^ represents the break-even point in dollars, and B.E<,P. is the break-even point in units, SP is the sellThe first equation is the more commonly used, for it expresses the break-even point in sales dollars, whereas the second formula expresses the break-even point in units for a particular product, provided a sum of fixed costs can be allocated to that product. This second formula cannot provide accurate results, for the VC (the variable cost per unit) is assumed to be constant. Additional variables would have to be introduced into the formula. Similarly, the variable cost ratio (VC/SP) or the marginal income ratio (1 3l£ for the first formula cannot be SP derived by using the unit variable cost and unit selling price. Now, if the total variable cost is to be used in the formula, an accurate figure can be determined only if the factor of experience is taken into consideration. The conventional total variable cost figure is likely to provide an inaccurate solution. This point can be illustrated by means of an hypothetical example. Table V-II presents production data for the first few units of a product

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212 oocMCMoooN.a-i'^cotnr^ ooo-j-uioomi^ 000-frOooiri'-'r^c^cOrooDforooooooooooo ooocooooooo ooooooooooo. -f OOOOOOOOOOO OOOOOOOOOOO OOOOOOOOOOO in o t^ 00
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213 representing a decline in cost with increased production. Assuming a selling price of $1,100 per unit, a conventional break-even chart can be constructed as in Figure V-1. It can be seen that using the conventional analysis, the break-even point is reached when sales of ten units take * place. However, taking into consideration the declining variable cost, the total cost line turns curvilinear and cuts the sales revenue line a little below the fourth unit. Thus the firm would break even when sales reach four units, and at ten units, a profit of $3,685 would be recognized. The same implications as evidenced in the above analysis could be connected with the direct costing concept, where all fixed costs are VTritten off as period expenses, and products charged with only the variable cost. Here, the ending inventory is calculated by ascertaining the quantity and multiplying the quantity times the price per unit. The possibility of varying costs per unit is not even considered, for the main constituent of varying cost per unit with quality is charged off as an expense for the period. This research seems to point out the possibility of a varying variable cost per unit, in which case different inventory valuation procedures such as Lifo, Fifo, average cost, etc., could conceivably be used for direct costing inventory valuation. If the flow of costs is assumed to follow the direction of flow of goods, which would be the more logical assumption in this case, then the inventory would be valued at a lovrer cost per unit, and higher unit costs would be charged to cost of goods sold, since costs would be declining with increased production. The research undertaken by this study strongly implies the importance

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215 of incorporating the factor of experience into conventional costing procedures and methods. The level of importance cannot be judged without empirical investigation into the specific production situation, and if found advisable, the procedures outlined by the preceding chapter should be utilized for more meaningful analysis. Implications for Planning The accountant is frequently called upon to provide management with qualitative and quantitative data which can be used for planning purposes. Information may be requested on various types of decisions, and the reliability of the accountant's figures is dependent on the degree of accuracy achieved in the process of accumulating and analyzing production information. Some implications of the experience factor as it affects planning needs have been discussed in this section. Forecasting labor requirements and plant loads, setting wage incentive schemes, budgeting for cash and funds, planning for capital equipment, pricing, purchasing, sub-contracting, and providing bases for decisions between alternatives such as m.akeor-buy situations are a few problem.s for which the managerial accountant may be called upon to provide his services. It would be pertinent to restate some of the observations made in the last chapter in connection with the planning process. Since the unit hours tend to be more erratic than the cumulative average, it might be m.ore advisable to use cumulative average projections in place of the unit hours for purposes of planning. The averaging process would provide a more stable function for purposes of extrapolating information, and it might not even be necessary to "derive " functions statistically from the set of data, for a

PAGE 225

B. E. P. (Conventional) 1 8 o I 7 CO^^ V?eV^<^' .A^ Ao' B. E. P. (Refined) Fixed Costs FIGURE Z-1 COMPARISON OF BREAK-EVEN POINTS WITH AND WITHOUT CONSIDERATION GIVEN TO THE IMPACT OF EXPERIENCE 3 4 5 6 7 1 Number of Units 10 11 12

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216 fairly smooth function can normally be expected, especially at higher quantities. Moreover, it is much easier to calculate requirements from the cumulative average than the unit hours. For example, the total number of hours expected for the production of N units can be arrived at by locating the point on the cumulative average curve and multiplying times N. Whereas to find the total hours from the unit hour curve, the conversion factor would have to be used to determine the cumulative average, from -where the calculation would be the same as stated above. In short, the cumulative average curve V7ith its suppressed dispersion, its fairly smooth projection, and its tendency toward a lesser degree of curvilinearity might prove more adaptable for planning purposes. Another implication to be stressed is the degree of reliability for extrapolated values. Various factors have an influence on the experience rate, and unless these variables are taken into consideration, the chances of determining accurate forecasts are doubtful. Extrapolated values further away from the actual data are more likely to error than closer am.ounts . The experience curve is more reliable as a tool for short-term forecasting than for long-range predictions unless distant unkno^ms are capable of quantification. Another tentative hypothesis can be stated. Pre-production planning can substantially contribute to the stability of the ensuing function. Hence, extrapolated values based on functions for well-planned products would be more reliable than those V7ith a lesser amount of pre-production planning. This hypothesis has not been empirically verified by this study.

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However, a conceptual analysis along with the research undertaken by this study indicates the possibility of better forecasting wherever well-planned products are manufactured. Forocastinr; for labor and plant rcquircnicnts Perhaps the subject for x^7hic^. the implications of continuous production on manufacturing time have been given the most recognition is the planning for labor and capacity requirements. The reliability of conventional forecasting procedures can be enhanced considerably by introducing the element of time reduction through increased production. Forecasting labor requirements is always a difficult task, but one which can lead to cost savings or wastages depending upon the accuracy of forecasts. Under the conventional calculations, the total hours per production unit may be forecasted, and then broken up into the number of men required to fulfill the task. The total hours for the first unit, or for the unit after production "settles dovm," or some form of an average is used to facilitate calculations for the units to be produced further on. Sometimes a rule of thumb is used to consider the effect of experience; at others, no attempt of any sort is made and the time per unit is taken as constant. To illustrate the effect, a simplified hypothetical example is used below. Let us assume a firm which wishes to produce OA units of a fairly complex product. Also assume that the production facilities are such that only one unit can be in production at a point of time. It is forecasted (or the actual time may be determined) that the first unit will take OH hours to assemble. If it is assumed that production time at unit one would be the same for all units produced, then OH hours per unit xrould be expected,

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218 In Figure V-2, the straight line HM indicates that hours per unit will be constant over the entire range of production. However, if the production time per unit, or the average time per unit, is assumed to be declining, and forecasted as the nonlinear curve HM' , then the number of workers needed per unit of production v.'ould be declining. If some form of an average per unit had been assumed, say H'M", compensating errors would result. L.^aereas in the first case more men would have been made available than necessary, in the third case, less workers than required would have been budgeted, at earlier stages of production, and more workers supplied than required in the later stages of production, for the actual requirem.ents would be around line H'M' . Similar analysis can be utilized for forecasting plant and space requirements, production scheduling, and settling more realistic delivery schedules. It could also be applied to forecasting requirements for special types of labor, for facilitating recruitment and training, for predicting indirect labor requirements, for overhauling and maintenance decisions, budgeting for engineering and staff efforts, etc. No attempt at illustrating the forecasting procedure has been made since literature abounds x^ith 12 all types and forms of examples. Establishing wage incentive schemes Over the years, several suggestions have been made to aid management in providing incentives for individuals and groups to reward special effort. Thus, schemes such as the Taylor plan, the Gantt Task plan, the Halsey plan, and the Bedaux-Point system were originated to serve as rewards for increasing the individual worker's efficiency, along with group incentive schemes

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219 Cumulativ* Units FIGURE 7-2 USAOE OF CONSTANT TIMES, COMPARED WITH DECLINING TIME PER UNIT FOR LABOR REGUIREMENT FORECASTING

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220 such as the Emerson Group plan. One of the troublesome problems in planning for these schemes is the setting of standards, for once the standards are set, the organization might be obligated to adhere to its proposals for fear of employee and union sanctions. This is perhaps the major reason for the trend toward profit-sharing plans and the apparent discardation of individual and group task schemes. In view of the discussion undertaken so far, it is not difficult to see why these schemes have proved unsuccessful. Setting a standard which is represented by an absolute value and which cannot be adjusted for the factor of im.provement could prove disastrous. For example, setting an "attainable" standard at the beginning might mean that with increased production the standard could be easily met and the company might end up with a sizeable labor payroll, for with increased experience even the most inefficient worker or group might soon cross the standard, and the very intent of the incentive might be lost. On the other hand, a "tight" standard might be encountered with opposition from workers and unions, even though it might prove to be a true incentive in the long run , Any absolute standard appears to be a poor basis for setting incentives. Some form of standard X'jhich can be reviewed and adjusted regularly to offset the decline in hours due to routine experience should be used, so that the more efficient worker or group can be rewarded without, at the same time, burdening the company with an excessive labor bill. Several plans have been suggested for incorporating the variable of increased quantity as it affects production time i.nio f.ho regular wage incentive schemes. It was pointed out earlier that a form of "learning

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221 curve" has also been used for this purpose. Thus Hadley has illustrated the use of "learner allowance curves" for compensating new employees dur13 ing their training period. A system for compensating efficient employees in situations where learners may affect group efficiency has been presented by L. A. Barron. In an experiment on clerical tasks, M. D. Kilbridge reported the observance of patterns which could be profitably utilized. Perhaps the most comprehensive system for dealing with the complications introduced by the factor of experience has been presented by Wertman , who indicates a method of adjusting standards to the level of production."^ The above references represent only a few attempts in the direction of adjusting standards, and the scope for research into proper systems for adjustment seems to be abundant. Budgeting for cash and funds Although it is conceivable that the impact of continuous production would be felt on cash and working capital, it can be argued that such an effect would be indirect, and in most cases, of an immaterial nature. It appears that the importance of the experience factor on cash and working capital planning is proportional to the value of the product. Thus, in the case of building construction, the impact might be of a more significant nature than in the manufacture of a small punch-press. Since the major source of funds is the product sales, and since this is dependent on the recognition of revenue which, in most cases, is dependent on the completion of the product, a fairly accurate forecast on the completion of the products is necessary to obtain a reliable working capital budget or a cash budget. It is not uncommon to find forecasts proving inaccurate due to non-recogni-

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222 tion of the improvement factor or inadequate rule-of-thumb applied for recognizing its effect. Blume and Pcitzke have indicated the importance of proper recognition for working capital requirements, and stron;;Xy imply that contractors, sub-contractors, and other producers should not treat this matter with any degree of laxness, for the im.pact of experience is strong, and taking the factor into consideration or not might determine the success or failure of ^. 17 a firm. Capital investment decisions A factor which is often disregarded in decisions regarding acquisitions of plant, discarding of equipment, or substitution of equipment is the experience factor. In the case of plant acquisition, alternative plans may have been formulated, and the final decision cannot be made without proper consideration given to the implications of improvement. For example, assume that alternatives A and B involve similar capital outlays; however, alternative A is believed to lead to a "lower cost per unit" than B. An important question is, how was this cost per unit arrived at? Some assumption regarding the volume of production must have been made. If averages of total expected production have been used for comparison purposes, then it can be argued that a m.easure of experience has been taken into consideration. However, the more usual procedure is to compare cost per unit for a smaller than optim.um level of production, such as cost at unit one or an average for the first hundred units, etc. If this be the case, the degree of scope available for improvement should be considered in the evaluation of alternatives. To continue the above example, alternative B might involve a complex production process leading to a higher cost per unit in

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223 the initial stages of production, but given sufficient time could more than offset the initial disadvantage through a later output at lower cost per unit. The implications of continuous production can and should be considered in the evaluation of capital equipment alternatives. In the use of methods for rating capital investm.ent alternatives, the rate of return, or the cash flow expected, can also be adjusted for the effect of improvement. As stated earlier, the calculations of cash flow and net income can be considerably affected by the process of averaging, and the proper effect of experience on cash flows and income can be adjusted for more efficient decision making. It is not uncommon to find an "average" annual rate of return or an "average" annual cash inflow being utilized for computation purposes. From the earlier discussions it is evident that such an average could be a dangerous figure to adopt, for the chances of positive returns in the initial stages of production are fewer than at later stages, especially under the presently accepted procedures for government and other large contract pricing. Pricing The problem of pricing is certainly connected with that of costing for products. Pricing of products may be approached by two routes. One method is to use the m.icro-economi.c marginal cost analysis, which is beyond the scope of this study. The other approach, which can be considered the accounting method, is to analyze the elements that contribute to the cost of a product and use an acceptable mark-up to arrive at the product price. Usually the term "cost" in this sense refers to the full cost; however, sometimes reference is to the variable cost only. In either case, the

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224 mark-up would compensate for other costs and profits. Making generalizations regarding pricing policies can be a dangerous thing; however, a few situations are analyzed below merely as examples, V7ith full recognition given to the limitations of such r.nalysis. Pricing the "regular" products of a company may not prove very troublesome, for if products are produced on an assembly-line basis, the implications of experience m.ay not be substantial enough to warrant recognition, or at the very most a rough rule-of-thumb m.ay be applied to "average" costs to offset any price differential. With an increase in the complexity of the production process, or in the production if fairly big and com.plex units, some form of recognition would have to be given to the decline in production tim.e and costs. Charging higher prices and reaping the additional advantages due to declining cost would have to be balanced against the rigors of competition. With extremely complex products such as airframes, computers, and building construction, the impact of increased quantities would have a definite role in the pricing policy. The decline in costs in these cases would be quite noticeable, and this is likely to give rise to peculiar problems. For example, having produced a certain quantity for a certain price, what should be the price to be charged for follow-on quantities? Assuming other things being equal, either the original price can be charged, or a smaller price to accomodate the decline in costs can be used. It is conceivable that this sort of situation could give rise to m.onopoly profits. For having produced a product for a customer, the firm might be able to quote a smaller price than another which would be new to the production

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225 process, and yet be able to price the product at a substantially large mark-up. A rather interesting implication has been pointed out by Asher in connection with the above point. '•° If it is true that experience leads to lower costs, then it would also be true that older firms would have a distinct advantage over any new entrant. This is not a nex^7 hypothesis, for it is well appreciated that older firms have an advantage over new firms through time to perfect their products and establish their names. To quote Asher :--^ The newcomer must also compete xvith producers whose cumulative output is relatively large, and thus close to a minimum unit production cost, or who are producing new lines sufficiently similar to older versions of their product as to result in low unit number one costs and hence, in relatively flat slopes. To compete with some hope of success, the newcomer must have substantial financial reserves so that he can sell his product at the current market price for similar-type products. This market price may be considerably below his production costs for some initial number of units. But with luck, and with sufficient financial backing, the nex-7comer may reach a cumulative output that will put him within reach of his competitor's production costs. The situation would be virtually hopeless, of course, for a newcomer in industry if the conventional linear progress curve were a more accurate description of the relationship between unit labor or production cost and cumulative output. That is, the existence (or assumed existence) of a minimum unit cost at least gives the newcomer an opportunity eventually to overtake his competitors. If no minimum unit cost were assumed to exist (other than zero), then the newcomer would have little chance of competing unless he were able to outproduce his competitors over a long period of time. Another interesting implication is the different prices charged at different times. Suppose an order is received from customer A for twenty units of a complex product, and a price is quoted for the lot. A few days later customer B asks for a similar product. Could a lower price be quoted

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226 to B in view of the decline in costs expected from the production for company A, or would this be considered as price discrimination liable to penalty under the Robinson-Patman Act? A superficial investigations points to the non-applicability of the legal restrictions, for it can be proved that differences in costs are involved, and hence different prices can be charged. However, the accountant would have to be well conversant with the quantification of the experience factor to be able to contest the charge successfully. Moreover, a proper understanding of the legal implications for pricing products where the factor of improvement is marked may be necessary. Further discussion on pricing is continued in the section relating to implications for purchasing and sub-contracting. Purchasing That the purchasing agents are becom.ing increasingly aware of the implications of increased quantities on production cost can be evidenced from the spat of articles published on the subject in the relevant periodicals. Countless illustrations have been dramatized to make purchasing agents aware of the potential savings to be derived from forcing vendors to pass over the benefits of declining cost to the purchasing firm. The situation is even more stressed in the case of partial assemblies, for there is considerable scope for cost savings through repetition of orders. In the selection of vendors a definite edge would be held by those experienced in the production of the particular product. Blume and Pietzke have presented a situation where a supplier had produced a thousand units of a product at a given price and it V7as decided to purchase two thousand

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227 more units of the same product. After making the necessary calculations it xcas found that only 55 per cent of the original price would have to be paid for the portions influenced by the impact of experience on the new units. They decided to continue their analysis further in order to determine the relationship between the old and the new price at different quantity increases. The results of their analysis have been presented in Table V-III, in which an 80 per cent experience rate was used for calcula20 txons. The importance of considering the experience factor for pricing and purchasing has not yet been fully appreciated, as can be evidenced by the apparent lack of concern for its implications in academic curricula, especially in accounting text books. Selecting between alternatives It is not uncommon for the m.anagerial accountant to be called upon to submit information which could aid evaluation of alternatives. Management, in order to perform its task of operating at optimum efficiency, is often faced with the dangerous task of making prompt decisions. Alternatives may be difficult to evaluate due to the lack of information available and this non-availability of data tends to introduce a considerable element of subjectivity and personal judgments. Hence, whenever any quantification is possible which could facilitate the process of evaluation, management might seek its aid through the accounting or the statistical sections. It is not unusual for the accounting department to be called upon to give information regarding decisions such as make-or-buy, assemble-or-subcontract, operate-or-lease, process-or-sell, determination of a combination of product

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228 TABLE V-III Relationship Between Increases in Quantatives Ordered and Their Resultant Prices % Increase on Quantity % of Old Price to Be (New Order Divided by Old) Paid for Nev; Order 10 67 50 63 100 60 150 57 200 55 500 48 1,000 41 1,500 37 Source: Blume and Pietzke, p. 9.

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229 mixes, addition or elimination of a product line, expansion or contraction of production facilities, temporary shutdoxm or continuation, permanent dissolution or reorganization, acceptance or rejection of special orders, or other decisions where financial and quantitative data could provide bases for more reliable evaluation of the alternatives. A few of these special decision situations, and how the experience factor can affect decision making are discussed below. Make-or-buy, operate-or-lease, assemble-or-sub-contract : Although the implications for make-or-buy, operate-or-lease, and assemble-or-subcontract situations could have been discussed along with the section on purchasing, exclusion was deliberate, for in these cases the alternative of utilizing the firm's production facilities is an added factor for consideration. It can be stressed that in situations involving make-or-buy and sub-contracting decisions, not only has the question of capacity and initial cost to be examined, but also the factor of "where" on the experience curve would the firm's production be as opposed to the potential vendors'. For example, disregarding the effects of capacity utilization, a vendor might quote a slightly higher price than it would cost our firm to make the product. Under conventional procedures one would tend to decide in favor of making the part rather than buying. However, the vendor's present production status may be in the initial stages of manufacture as opposed to a considerably experienced facility operated by the producing firm. That is, the vendor may be on a steeper experience curve slope, so that after a certain number of units has been produced, the parts may be made available at a lower price than it would cost the firm.

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230 In a similar fashion, it is also conceivable that temporary "switch-over" decisions may be affected. It is not uncommon for firms to produce products whenever capacity is available and then "switchover" to a supplier for the same product on the grounds that such a move is temporary, and production is to be continued whenever facilities are available. In such a case, an extra cost might be added to the production of the replacing product or part to compensate for the loss of experience on the original part due to the lay-off. To look at it from another angle, any time a decision has to be made regarding changing vendors or buying rather than making, with the intention of reconverting back after a lapse of time, the impact of a lay-off on the producer's facilities should be taken into consideration. It would appear that the above assertions may not be important, especially for sm.aller firm.s, and this might very well be true; however, one cannot assert a priori that such would necessarily be the case. Only an investigation into the particular conditions would determine the relevancy of the implication. An illustrative example of the impact of experience on decisions of this nature has been presented by Frank Andress, and since the situation represents an actual case (with disguised company names), it has been 21 reproduced here in its entirety: Early in 1952 the Lee Aircraft Company was faced with a cutback in its production as a result of the Air Force stretchout program. Consequently, it was inclined to cancel some of its sub-contracts and pull the work into its o\-m shop to keep it fully occupied. One subcontract which it thought of canceling V7as with the Roberts Manufacturing Company for 372 landing flap assem.blies — an item which it also was manufacturing in its o\m plant. To arrive at a comparison of its otto and Roberts' costs of manufacturing the assemblies, Lee decided to plot the respective learning curves.

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231 Lee had already produced 165 assemblies, with a figure of 445 hours for the 165th unit, and was well along the downward slope of its learning curve; continuation of the curve indicated a total labor input of 111,000 hours for 372 additional units. In comparison, the Roberts Company, while apparently a more efficient producer of the item, was just getting started on its learning curve; if it went on, it would be able to produce the 165th unit at an expenditure of 402 hours — 43 hours less than Lee — but continuation of its curve from the earlier, higher point at which it then was indicated a total labor input of 164,000 hours for the 372 units, or 53,000 more than Lee. The foregoing analysis served a pinpoint the question for management's judgment. In the short run, it was more economical for Lee to cancel the subcontract and do the work itself. In the long run, however, it would be less expensive to leave the work with Roberts inasmuch as it could produce the landing flaps for about 10% less labor since it had got as far out on its learning curve as Lee. Therefore, the decision hinged largely on the probably total future demand for landing flaps of this type. Since this total future demand was difficult to measure, Lee decided to take advantage of the direct labor savings offered at the time, which amounted to over $300,000. Accordingly, it canceled the contract with Roberts. The problem of operating a department or leasing out at a fixed rent can be analyzed in the same manner as above. Process or sell : The course of action to be taken in a situation where a product can be sold at an intermediate stage of production, or further processing could be undertaken to sell it at a different price, could also be influenced by the factor of experience. For example, an investigation might indicate that a product presently saleable at a net profit of five dollars per unit could be further processed and sold at a net income of four dollars a unit. The initial reaction would be to reject the proposal for further processing. However, the new process might generate its own decline in costs with increased production, in which case, the net income per unit after a certain amount of production has

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232 been attained might increase to over six dollars a unit, or more, depending on the level of production attained. In such a case, taking into consideration the effect of continuous production, a different solution might emerge. Product combination : Management is always faced with the problem of selecting a combination of products which xTOuld be the most profitable under the given conditions. Thus, decisions have to be made regarding the ideal quantity of products presently produced, adjustment of specific varieties, introduction of new lines, curtailment or elimination of old lines, etc. Generally the contribution margin theory is applied to determine the product m.ix. Thus, the variable cost per unit is ascertained, Xv'hich is deducted from its selling price, to arrive at the contribution margin. The contribution margin per unit can be converted into the contribution margin per hour, evaluated in relation to the restraints imposed by the 22 market and production facilities, and the best combination determined. From the above procedure it can be witnessed that the decision involves the quantification of labor hours in order to arrive at the total variable costs, and also to determine contribution from the entire production. If experience can affect production times on the various products differently, the decision would have to be made taking into consideration the quantity to be produced, and the decline in costs xvith increased quantity. Conventional analysis should be adapted to allow for the factor of experience in decisions regarding product combinations. Expansion, continuation, and shutdoxm decisions: The problems of

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233 expansion and continuation are not as difficult to deal with as those posed by curtailment of activity, either as a temporary cut-back or shutdown, or a permanent dissolution situation. In the case of expansion, either extra facilities might be added (which would come under the capital investment decision), or the present facilities may be more intensively used. In the later case, multishift operations may be resorted to. However, it should be remembered that an additional shift cannot produce the product at the same price as the regular shift. This is often recognized by managerial accountants for particular analyses. For exanple, labor may have to be paid a shift differential, manufacturing overhead costs of repairs and maintenance may not increase in proportion to output, materials may be bought at higher quantity discounts, etc. What is not recognized is that an introduction of a new shift might necessitate the introduction of new crews and inexperienced men, and the production time taken by these new crews may not be anyrvhere near the time taken by experienced workers. If contracts are obtained at prevalent prices, with the hope that greater production could be achieved through the starting of new shifts, the resultant profits might not indicate the success of such a move to the extent anticipated. To put it mildly, the product output cannot be expected to double by changing from a one-shift to a two-shift operation. Similarly, in decisions regarding a temporary shutdown, the effect of the closure on the transfer of experience has to be taken into consideration along with the factors used in conventional analysis. If facilities are to be reopened, the costs to be expected on the commencement of operations have to be adjusted for the loss of experience.

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234 In conclusion, it should be pointed out that the discussion undertaken on planning does not invalidate or belittle any of the conventional tools and methods. It merely points out that the value of these procedures could be enhanced significantly if the implications of continuous production on time and costs are taken into consideration. Implications for Control In the process of research for this study, it was observed that most of the attention given to the implications of experience was for its probably applicability in the area of planning. Very seldom, were its implications for purposes of control referred to, and only a few references indicated an awareness of its potential. The position taken by this study is quite the opposite. It is believed that the factor of improvement from continuous production can be utilized very profitably for the function of managerial control. It is a contention of this study that the implications of the experience factor can prove a valuable tool to aid the function of control; and whereas the process of planning certainly can utilize the quantification procedures, the potential for control is as much, if not more, promising. This section indirectly provides evidence in support of this contention. Primary emphasis has been placed on an investigation of the conventional usage of production control charts and procedures and the use of standards, standard costs, and variance analysis. Implications for evaluation of employment practices, judging supervisory and managerial efficiency, ascertaining the effectiveness of value engineering or cost reduction plans, etc. have also been commented on briefly. Above all, procedures for aid-

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235 ing managerial control have been indicated throughout the section. Before delving into the specific implications, it might be worthwhile to review some of the observations made in Chapter IV. It was noticed that the cumulative average function tended to smooth out the observed deviations between unit hours. This averaging process is most unsuitable for purposes of control, for the principle of management by exception is based on the investigation of abnormal deviations; that is, control is possible only if variations can be observed and pointed out for investigation and possible remedial action. Hence, it would be the individual unit hours or costs which would be more acceptable for purposes of control. The unit hours can be plotted and studied to notice irregularities, for, provided consistent data accumulation procedures have been used, any marked deviation would provide a basis for investigation. Once again, the plotting can be done on arithmetic or logarithmic grid paper. It would appear that plain arithmetic grid graph paper V70uld be preferable for indicating deviations, for the points would be almost overlapping on logarithmic grid paper at higher levels of production, whereas on arithmetic grids the deviations would be more pronounced. It can be argued that the length of paper needed for plotting on arithmetic grids would be absurd as indicated in Chapter II. However, the problem of excessive length can be solved by changing the scale of the abscissa. Production time control charts and procedures Various types of charts and reports are used for purposes of controlling operations, and although the majority of such charts belong to

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236 the quality control variety, the accounting department can aid management by furnishing quantity control measures. In the words of J. R. Crawford : Control . . . can be accomplished best through the medium of m.anufacturing accounting records. Although forecasts are laid out in figures and measured against figures furnished by manufacturing accounting, the true relationship is seen only when these figures are plotted on charts. Trends and patterns can be established from these plottings, and the measure of performance against commitment can then be easily observed. 23 The accountant may be called upon, among other things, to aid in the introduction and upkeep of charts which signify the efficiency of operations. One way to measure efficiency is to present a chart with a line drawn horizontally depicting the expected hours or costs per unit, and as each new unit is completed, its completion time may be plotted on the chart to mark its relative position to the anticipated mean. However, if the impact of experience is significant for the production process, this conventional procedure m.ay prove ineffective. For if average time is used, the initial units produced would tend to indicate an unfavorable balance and could be m.istakenly labeled as inefficient production. On the other hand, once production has settled dovTn, the unit hours for the subsequent production might be labelled as efficient even though such might not be the case. This situation can be better explained with the help of an example. The set of data used for purposes of analysis in Chapter IV is used again, with an added piece of information. It will be assumed that after a detailed engineering and time and motion study, it is determined that a unit should be assembled in 5,050 hours. This figure would then represent the mean and can be plotted as

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237 a straight horizontal line on plain graph paper as sho\m by line AB in Figure V-3, and on logarithmic grids by line A'B' as in Figure V-4. As the actual times taken on each unit are accumulated, they can be plotted on the graphs to determine their position in relation to the expected production time. If the unit hours presented in Tables IV-I and IV-II are plotted on arithmetic or logarithmic grid paper, the plots V70uld appear as shoxm in Figure V-3 and IV-4 respectively. A cursory glance at the figures indicates that there is nothing drastically wrong xjith the production process, for almost all the points are around line AB and A'B' . However, if it is assumed that the first twenty units were produced under normal conditions, and if it is anticipated that future production should follow the trend indicated by these twenty units, then it v7ould be the extrapolated line indicated in Figure IV1 and IV-3 which should be the basis for control. The magnitude of the deviations is much m.ore marked when the extrapolated lines are used, as shown by curves CD and C'D' in Figures V-3 and V-4, for most of the later twenty-five units fall above the trend, indicating the possibility of disruptions. Which would be the more reliable control line to use — the static unit hour line stated in the form of an absolute figure or the declining curve which takes into consideration the implications of experience? Using the constant hours per unit line, no cause for investigation is indicated, and if the principle of m.anagement by exceptions is to be utilized, no reason for bringing observed deviations to m.anagement ' s attention can be seen, for all the plot points are centered around the mean. However, using the derived declining function, cause for investi-

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2ds o e o X ^ a. O < go < o s: »« m

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,^3 9 /

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240 gation can be noticed immediately, brought to the attention of those in charge, and control procedures initiated to understand and, if necessary, correct the deviations. In the example used above, it is quite evident that a drastic change took place after the first nineteen units. For example, a considerable amount of time might have elapsed between the nineteenth and the succeeding units, or a major design change m.ay have been undertaken, the assembly locations might have been shifted, more crews introduced leading to a mixing of inexperienced with experienced workers, etc. An investigation might indicate the advisability of replotting the data on a different graph and considering the product as a new one. If the change cannot be considered as substantial, the same graph can be used with an awareness of the fact that the recognized change affected the trend. It is not necessary that deviations should result only when abrupt changes take place. The curve m.ay steadily flatten out, in which case the declining trend would bring this to management's attention much more efficiently than the horizontal line. The flattening-out may be due to factors indicating controllable inefficiencies, such as monotony from working on a stereotyped assembly. If such deficiencies are controlable, management can use its position to remedy the situation. For example, the problem of monotony could be solved by revitalizing interest through the provision of incentives, shifting workers around, changing supervisors, etc. Moreover, it is not necessary that the extrapolated trend be linear. A curvilinear trend, if found to be a more significant fit for

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241 the set of data, could be conveniently utilized. It is important that the pol3momial analysis be applied periodically to the actual data to determine the most significant fit. If the tests indicate a curvilinear fit, reasons for this can be sought and better control achieved. The point to be noted is that a trend taking into consideration the implications of experience can be a more reliable tool for control than the conventional form.. Vincent J. Shroad, Jr., has presented a chart reproduced in Figure V-5 which indicates the possibility of utilizing cumulative data for purposes of cost control. The graph indicates that the increase 5.n cost experienced after the first thirty units were produced (as shotm. by the total hours line), was primarily due to the higher cost experienced by the inspection department. The impact of increase in inspection hours was felt m.uch more on the total hours than on manufacturing hours, for only indirectly would inspection affect manufacturing. However, a graph such as this could aid control by pointing out the trend and discrepancies for prompt action. Sim.ilar charts can be constructed for each product, with a breakdot'Tn by elements, operations, departments, or even specific cost centers. The greater the subdivision the greater the scope for control. A case history of an attempt at applying the experience factor for control reporting has been presented by Julian L. Kottler of AVCO Corporation, who has illustrated the use of plain graphs along with the logarithmic graphs to achieve control. An interesting illustration, from the accountant's point of view, is a detailed periodic cost report presented by Kottler. This report summarizes various pieces of information

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Jl^^ Total Hours Total Hours Or Cost Affected 3y Increase in Inspection And Tightened O.C. Requirements ted 8, Total Indicated Trend. /n sp ecfj •Manufacturing Hours qui "^Ss

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243 which might be considered important by management, such as the equivalent units on order, quoted amounts, planned cost, actual program status, estimate of completion, and estimated final cost for the entire program and for each major operation separately. The element that differentiates this report from the conventional one is that the planned and estimated figures are all expressed after consideration has been given to the element of continuous production. A further aid to the control of operations xcould be the use of confidence limits on the charts. Engineers and quality control analysts have used confidence intervals for decades, and their application for quantitative analysis is widely accepted. These confidence limits can be used on the production tim.e control charts to point out significant deviation and marked trends in a more efficient manner. The confidence interval specifies the area xdLthin xvhich the unit times must fall. If points fall beyond the interval, this would be a signal for investigation and corrective action. The confidence attached to an interval is measured by an objective probability that is considered acceptable for purposes of analyses. Thus, a 90per-unit confidence interval signifies that 10 per cent of the plot points may fall outside the confidence belt. These 10 per cent of the units will be outliers or exceptional deviations which can be investigated. The probability coefficient, in the above example 90 per cent, can be selected by the management or the analyst in relation to the degree of control deemed necessary. Thus, if strict control is to be maintained, a 66.6 per cent confidence limit may be set. On the other hand, a 99 per cent confidence interval would im-

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244 plicate only the very extreme deviations, leading to a lesser degree of control. Glen E. Ghormley has indicated how confidence or control limits can bo used for ascertaining and correcting deviations from the expected 27 trend. Using arithm.etic grid graph paper and daily production instead of hours per unit, he has extracted a trend line and set the confidence limits as shoTim in Figure V-6. Since the number of units produced per day would be increasing with the experience gained, other things being equal, the trend line would be upward sloping, and so would the confidence lim.its be positively sloped. From the chart it can be ascertained that the first two do^mward bleeps were for repair stoppages, probably an uncontrolable deviation. On the other hand, the decline in daily output after September 19 is due to worn tooling. This decline would be a sign for management to take action and replace the necessary tooling before further decay or a complete stoppage takes place. The control limits have been shown as straight lines in the above illustration. However, for more accurate limit setting, advanced statistical tools can be used to obtain a more reliable confidence limit. Statisticians have indicated that a more accurate confidence interval is composed of curvilinear limits with the ends being wide open and the limits approaching the trend line around the middle of the chart. An example of how these limits can be set has been presented by Wallis and 99, Roberts. Standard costing and variance analysis The accountant can aid management by developing a proper system of

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/^J UJ CM O Q O Z o ^ o "

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standard costing, and supplying relevant information regarding variation between predetermined standards and actually incurred amounts. The efficacy of standard costing as a control tool is determined by the fact that the standards set are based on scientifically regulated techniques. Standards expressed in physical quantities, or standard costs expressed in monetary equivalents of the physical quantities, represent the amount that should be incurred. Thus, when the actual quantities observed are compared to the predetermined standards, all variation can signify disequilibrium. Under the management by exception principle, any significant variation is to be reported and serves as a basis for action. From the above recapitulation, it can be noticed that the setting of standards would be an important determinant of the effectiveness of the system as a basis for control. Hence, the important question is: how are the standards set? Basically, each element of m.anufacturing cost is studied for its constituents, and various forces affecting the elements dissected and analyzed. Thus, the major constituents of material standards are the price and the quality of materials which can be considered the ideal amounts for a product or process. The labor content and the rate at which that labor should be remunerated are utilized in setting labor standards. The manufacturing overhead standards pose a different sort of problem, for costs included in this category include fixed as well as variable elements, and hence standards are set taking into consideration the capacity, expected level of production, and anticipated expenditure for that level. Since the implications of experience on fixed costs are considered insignificant, and since variable manufacturing overhead is

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247 assumed to have a definite relationship with direct labor, it has been found advisable to concentrate on the implications for material and direct labor, with very little attention being given to manufacturing overhead. The actual procedure for setting standards has been stated by Stanley B. Henrici as: Ideally the standardizing preceeds the establishing of the standard costs. The supervisors and engineers of the company examine the various jobs and determine how each task should be done, then standardize its performance on the basis of time and methods studies. After this has been done the standard cost accountant translates this standardization into dollars and cents and provides a means for measuring the cost of failure to adhere to it. 29 To illustrate the point, the setting of standards for labor requirements is considered here. Henrici indicates that there are several techniques available for setting these standards. These techniques include an analysis of historical records, simple observations, time-study, predetermined time standards, and work sampling. By each of these methods some form of absolute figure can be presented as the standard, Henrici' s enumeration does not differ significantly from other authors. For example, Cecil Gillespie asserts that three methods can be used for scientific standard setting: time study, comparison with similar opera31 tions, and developing special formulae. Once more, absolute standards are the results, even though Gillespie's formula approach takes into consideration a few more variables than plain time and motion study. Microscopic or macroscopic means can be utilized to study the operations involved before a standard is set. However, the fact remains, irrespective of the means used, that the final figure is stated in the

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248 form of an absolute. Thus, it may be stated that an operation should take X hours, irrespective of whether it is a relatively new operation or one which has been performed beforeIf the operation is performed in X + Y hours, it is indicated as an unfavora.ble variance. On the other hand, if the operation is completed in X Y hours, a favorable variance is said to have resulted. The limitations of this conventional procedure is apparent, especially when one considers the fact that standards are not to be revised unless "substantial" irregularities are noted, or a "reasonable" length of time has elapsed between the setting of the standard and its revision. A consideration of the different variances makes it apparent that the labor efficiency variance and the material usage variance would be the two most likely to present an erroneous basis for control. This can be illustrated with the help of an example. It is assumed that the standards have been set after a detailed investigation using the most scientific techniques. The standard for manufacturing and assembling one unit of a product is set at 200 labor hours. It is an accepted practice that once a standard has been set, it is to be used for a substantial period of time. Now, if the "ideal" standard is set using some kird of averaging process, and if production is influenced by the factor of experience, the resultant variance might be misleading. Tlie actual time taken on the first few units would be m.ore than the standard, indicating unfavorable variances; on the other hand, the standard would be higher than the actual reported tim.e after production has settled doxm, indicat-

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249 ing a favorable balance. In actuality, both these judgments might be invalid. If the production was subject to an experience rate of 70 per cent, the conventional variance analysis would give •^vorong results as indicated in Figure V-7. Any point falling in the area sho^m. on the graph where the actual is greater than the standard would be considered as an unfavorable variance under conventional standard costing. However, if the experience factor could be properly quantified and its effects considered, points falling in the same area would be looked upon as favorable variances rather than unfavorable. Similarly, unit hours falling in the area where the standard is greater than the actual would be considered as favorable under conventional procedures, but as unfavorable using the refined approach. Furthermore, the magnitude of variances could also be better visualized if some sort of declining standard could be used in place of an absolute figure. An alffiOst identical analysis may be conducted for noting the implications of experience on material quantity or usage variances. The quantity of raw material needed for providing one unit of a finished product in the early stages of production would not be the same as that used after substantial production has been undertaken. Hence, what m.ight look like an acceptable unfavorable balance, might in reality be a highly unfavorable variance which should have been reported for necessary action. The material price variance, labor rate variance, or the overhead variances could be similarly affected, although the extent and importance of affliction would not be in the same category as the two discussed above.

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^50 c

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251 It is surprising to note that no mention of the implications of experience on the setting of standards or on the evaluation of variances 32 was found in any advanced work on the subject. Only on the very last page does Henrici list "improvements in existing processes" as one of 33 the factors that could lead to a revision of standard costs. To point out a weakness without indicating possible solutions would not be the proper approach for any research project. On the other hand, to formulate a theoretical solution without adequate empirical verification is also open to the "lack of practicability" criticism. The latter guilt appears to be less harmful than the former, and hence possible solutions to supplem.ent existing procedures are indicated below. In the case of products and processes where an immaterial impact of experience is evidenced, it might be advisable to use conventional procedures without any alterations. Similarly, in production situations where a product has reached a considerable level of production, the impact of experience may not be given any recognition. Wherever it is noticed that a possibility of the experience factor affecting control procedures might exist and yet it can be witnessed that the impact is not substantial, recognition to the factor may be given by means of more frequent revisions. Thus, where production has been started but is not considered as "standardized," frequent revisions may be relevant. However, in the case of nexvr products and processes, where the standards have only recently been set, or where a noticeable decline in production time is mtnessed, m.ore drastic steps may be required. If the rate of decline is fast, it would be advisable not to use an abso-

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252 lute standard, but to use control procedures such as a variation of t!ie chart indicated in the previous section. Thus, for the material usage variance, a chart may be constructed utilizing a declining quantity of raw material to be allowed per finished product, so that true efficiency can be noted. For labor efficiency, a declining time per unit may be allocated, and actual times collected checked against the estimates. In other words, a sliding scale standard may be substituted in the place of an absolute figure. Another means for dealing with the problem without using a chart would be to use a mathematical form.ula to introduce the sliding scale. The formula should be such that with every unit produced the standard V70uld be reduced to take into consideration the quantity produced. This would involve using a geometric scale that would be adjusted with every additional information regarding quantities produced. If computer facilities are available, this procedure could be profitably utilized; otherTd-se, manual calculations might prove to be a major obstacle for effective usage, A more "practical" but less accurate procedure would be to indicate on the cost card different standards for limited production levels. Thus, one standard may be stated for units one to ten, another for units ten to fifty, a third for units fifty to one hundred and fifty, and so on. This could facilitate variance analysis and make it more reliable than conventional procedures. Yet another alternative vzould be to set up an index, which could be referred to while analyzing variances. That is, an absolute standard

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253 may be used, and variances calculated in the usual manner. However, before reporting variances, these may be checked with the index in which the percentage of variation which may be considered as normal for that level of production. Only those variations indicated as abnormal would then be reported for action. The index would have to be set up, taking into consideration the level of production at which the standard was set, the expected rate of im.provement, and the quantities of production anticipa^ted. These are only a fe\
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254 If a design change :.' to be initiated, it is important that the effects of the change be quantified in the conventional manner for costing and pricing. However, it would be even more important to check the effect of experience on the changed product, for if the change leads to a different experience rate, the cost and price of subsequent units might have to be adjusted. If the change is "substantial," the product can be considered a new one, and using a "B" factor (as explained in Chapter II) to compensate for partial experience gained, a new graph can be drawn. However, when can a change be considered "substantial"? The results of this study indicate that if data on a product are plotted after a design change, and it is noticed that the subsequent plots do not fall into the pre-change trend after a few units have been produced, the product can be considered as new. In other words, if, after the initial scallop, the post-change hours do not follov? the pre-change trend, a "substantial" change has taken place, which would necessitate a new graph. This would mean that calculations of costs and prices might have to be adjusted to account for the change in the rate of improvement . The importance of this aspect can have implications for planning and policy establishment, as indicated by a study made on the American shipping industry, which asserts that "standardized design will prevent unnecessary variations in design factors and constructional variations — savings up to $1,000,000 per ship can be expected. ... It may be well for all to consider what can be done with standard designs to obtain the ,35 overall economies which come from group production.'

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255 Some benefits of continuous production have been prominently listed, among other factors, that can lead to cost reduction from, standardization. The technical aspects of measuring design changes have been demonstrated by various authors, and hence have not been illustrated here. Other control applications In a series of articles published in Western Industry , Glen E. Ghormley has demonstrated the use of dynamic relationships for various control tools and concepts.'^ Although the author has been, for the most part, preoccupied with the influences of the individual Xv^orker, several interesting points em.erge from his discussion. In the second article of the series, Ghormley illustrates the results actually obtained in a comparison of supervisory ability on workers' output, and concludes that erratic, flat, or upward sloping curves are obtained for workers under poor supervision. This means that supervisory capability can be judged by using dynamic data. In the third article, a poignant point is brought out regarding evaluation of worker efficiency. Figure V-8 presents production data for four workers who started on a job, each taking a different amount of time to complete the first unit. It was determined that both A and B had no previous experience, C had ten years' experience but was laid off for six years, and D had one-and-a-half years' experience and a year's layoff. Under conventional procedures, or where workers are selected on their performance on a "trial run," a choice between A and B would have led to A being retained. Similarly, a choice between C

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4!un JOd su' o

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257 and D would have led to C being retained. However, given time to express their capability, it can be seen that B and D would be the better choices, for they "learn" faster than A and C. The above illustration brings out the point that the capabilities of individuals and groups at a point of time may not be the best basis for judging future potential. T-Jherever ti.me and opportunity is available, the dynamic element should be studied for trends and patterns to aid better decision making. For example, more experienced m.en might be preferable for short-run type of jobs whereas less experienced but spirited vrorkers may be found more acceptable for long-run jobs. Of course, no judgm.ent can be made without taking into consideration the rate of remuneration. Quality control is another area where the implications of continuous production can be accounted for; however, no comment is made here on this point for the subject is beyond the scope of this study. While commenting on material standards, it was implied that wastage and scrap would be influenced with increased production. In that connection, it can be noted that James M. White has demonstrated the applicability of the experience factor for aiding control by means of allowed "percentage 38 of wastage" allowances. The efficacy of cost-reduction schemes and value engineering programs can also be viewed more realistically if the influence of experience is properly quantified. However, the actual impact of improvement on the measurement of these programs is difficult to conceptualize without empirical data with which to experiment.

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258 In conclusion, it can be stated that the implications of the experience factor hold considerable potential for a more reliable measurement and control of business operations; and wherever possible, the procedures outlined earlier in this section should be utilized for increased efficiency in aiding the function of managerial control.

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259 FOOTNOTES Chapter V 1. T. P. Wright, "Factors Affecting the Cost of Airplanes," Journal of the Aeronautical Sciences , III (February, 1936), 125. 2. H.Asher, Cost-Quantity Relationships in the Airframe In dustry , R-291 (Santa Monica, California: The Rand Corporation, July 1, 1956), pp. 114-115. 3. •. Wilkerson, "Application of Learning Curve Techniques to Audit," The U. S. Army Audit Agency Bulletin (June, 1964), p. 50. 4. E.C. Keachie, and R. J. Fontana, "Effects of Learning on Optimal Lot Size," Management Science , Series B, XIII (October, 1966), 102-108. 5. Asher, o?. cit ., p. 117. 6. G. E. Ghormley, "The Learning Curve: Fitting theWorker to the Job," Western Industry (Decem.ber, 1952), pp. 47-49; A. R. Knowles and L. F. Bell, "Learning Curves Can Save You Time and Money," Factory Management and Maintenance , CVIII (June, 1950), p. 115. 7. The result of one such study has been reported by M. D. Kilbridge, "Predetermined Learning Curves for Clerical Operations," The Journal of Industrial Engineering , X (May-June, 1959), 203-209. 8. R. Brenneck, "Learning Curve Techniques for More Profitable Contracts," N.A.A. Bulletin , XL, Sec. I (July, 1959), 66-67. The procedure explained below has been adapted from Brenneck' s detailed example. 9. V. J. Shroad, "Control of Labor Costs Through the Use of Learning Curves," N.A.A. Bulletin , XLVI, Sec. I (October, 1964), 15-17. 10. C. L. Moore and R. K. Jaedicke, Managerial Accounting (Second Edition; Dallas, Texas: South-Western Publishing Co., 1957), p. 554. 11. R. Brenneck, "B-E Charts Reflecting Learning," N.A.A. Bulle tin , XL, Sec. I (June, 1959), 34. 12. To indicate a fev: references: P. B. Crouse, "Projecting Labor Loads in Aircraft Production," Aero Digest , XIIII (October, 1943). 216-218 and 242-243; J. Chassan, "Estim.ating Director Labor Costs in Aircraft Production," Industrial Aviation , III (July, 1945), 55-62; S. B. Smith, "The Learning Curve: Basic Purchasing Tool," Purchasing

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260 (March 11, 1965), pp. 70-75; and R. B. Jordan, "Learning How to Use the Learning Curve." N.A. A. Bulletin , XXXIX, Sec. I (March, 1962), 27-39. 13. J.R. Hadley, "Learning Curves on Log-Log Paper," Advanc ed Management , XV (April, 1950), 15-17. 14. L. A. Barron, "Learner Curves Boost Team Output," American Mechanist , CII (December 1, 1958), 100-101. 15. Xilbridge, op. cit ., pp. 203-204. 16. L. Wertman, "Putting Learning Curves to Work," The Tool Engineer , XLI (September, 1959), 100-101. 17. E. J. Blume and D. Peitzke, "Purchasing V7ith the Learning Curve," North American Aviation, Inc . (August, 1953), pp. 11-12. 18. Asher, op. cit ., p. 139. 19. Ibid., pp. 139-140. 20. Blume and Peitzke, op. cit ., pp. 8-9. 21. F. J. Andress, "The Learning Curve as a Production Tool," Harvard Business Review , XXXII (January-February, 1954), 353-354. 22. Moore and Jaedicke, op. cit ., pp. 511-514. 23. J.R. Crawford, "Statistical Accounting Procedures in Aircraft Production," Aero Digest , XLIV (March 15, 1955), 78-81. 24. Shroad, op. cit ., pp. 176-180. 25. J. L. Kottler, "The Learning Curve--A Cast History in Its Application," The Journal of Industrial Engineering , XV (July-August, 1964), 176-180. 26. W. A. Wallis and H. V. Roberts, Statistics: A New Approach (Brooklyn, New York: The Free Press of Glencoe, Inc., 1956). 27. G. E. Ghormley, "The Learning Curve: IV," Aero Diges t, XXXIX ' (August, 1941), 18-19. 28. Wallis and Roberts, op. cit . 29. S. B. Henrici, Standard Costs for Manufacturing (Third Edition; New York: McGraw-Hill Book Company, Inc., 1960), p. 128.

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261 30. Ibid., pp. 130-133. 31. C. B. Gillespie, Standard and Direct Costing (Englewood, New Jersey: Prentice Hall, Inc., 1962). 32. It must be admitted that only a limited amount of research was conducted on this aspect. Some of the works referred to were A. Danielsson, On Measurement and Analysis of Standard Costs (Stocldiolm: The Business Research Institute, Stockholm School of Economics, 1963); J. Batty, Standard Costing (London: MacDonald and Evans, Ltd., 1960); Henrici, op. cit .; Gillespie, op. cit . 33. •Henrici, op. cit ., p. 390. 34. L. H. Hall, "Experience with Experience Curves for Aircraft Design Changes," K. A. A. Bulletin , XXXIX, Sec. I (December, 1957), 59-66. 35. L. C. Hoffmann and C. C. Tangerini, "Reducing Costs of American Ships," a paper presented at the Annual Meeting of the Society of Naval Architects and Marine Engineers (New York, November, 1961), pp. 9-11." 36. H. R. Krocker and R. Peterson, "A Handbook of Learning Curve Techniques," The Ohio State University Research Foundation (Columbus: 1961), pp. 40-46. 37. G. E. Ghormley, "The Learning Curve," Western Industry (a series of four articles — September, October, December, 1952 and February, 1953. 38. J. M. White, "The Use of Learning Curve Theory in Setting Management Goals," The Journal of Industrial Engineering , XII (November-December, 1961), 409-411.

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CHAPTER VI SUMMARY AND CONCLUSIONS The purpose of this study was to investigate the implications of experience for managerial accounting tools, techniques, and concepts. The effects of continuous production on manufacturing time and costs were noted, and the implications analyzed. This was accomplished by an initial investigation into the work already done in the field, followed by a critique of presently accepted hypotheses. In the course of the last mentioned analysis, it was noted that the terra "learning curve" currently used to describe production time-quantity relationships is a misnomer, and the potential of dynamic data analysis should not be constrained by its narrow connotation. An analysis of the implied assumption of the experience curve "theory" indicated that under a continuous manufacturing situation, the product, the production equipment, and the process of data accumulation were to be considered constant, so that the minor changes or improvement v;ould be indicated by the declining labor hours or costs. A minor variation in product or process could be incorporated in the same function, vhoress a substantial change would necessitate a new product definition. Under such conditions the experience curve "theory" hypothesizes that production time or costs should decline at a constant rate with duplicated production. It was noted that this implied hypothesis of the business experience curve or the manufacturing progress function could not be accepted 262

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263 as a universal proposition, for conceptual as well as existential evidence was available which challenged the warrantedness of the assertion. In the first place, it was noted that a dynamic function was a composite of several elements, sub-elements, and so forth, each of which might be subject to varying rates of improvement. Thus, the unit cost function would normally represent the aggregate of several different elements of cost such as material, labor , and overhead; the direct labor hour curve would be composed of assembly time, sub-assembly time, and parts manufacturing hours, with each element being influenced at a different rate by the factor of continuous production. With the aid of simple mathem.atics , it was indicated that a function which represented a summation of different functions with varied rates would be curvilinear, even if the individual elements were straight lines. Furthermore, no "scientific" reason could be evidenced for improvement to follow the hypothesized pattern, since numerous variables were found to be involved which could, individually or collectively, react in unascertainable ways. Empirical investigation also seemed to indicate the existence of different forms for dynamic data projections. Varied forms reported by analysts were grouped to exemplify the possibility of non-linear forms. Thus, linear unit hours, cumulative average, and lot average curves were illustrated and explained along with their non-linear counterparts. Also, an inverted "S" curve, a humped projection, a convex possibility, toe-up, toe-down, and levelling-of f peculiarities, a straight line on semi-logarithmic grids, and a no-trend indication with resultant functions after reclassification, were individually

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264 discussed. In addition, brief reference was made to dynamic data analyses incorporating additional variables. Thus, P. Guibert's introduction of the rate of output as a variable was noted, along with the incorporation of design changes for better forecasting as propogated by two industrial engineers. The accountant's role in the accumulation, classification, interpretation, and reporting of dynamic production data was also investigated. It was noted that the above tasks v;ere within the preview of an accountant's job, and although special care was needed for quantifying the implications of experience, no unsurmountable difficulties could be evidenced. Factors which should be taken into consideration by the accountant in the recording and interpretation of dynamic production data have been summarized below: 1. The production data reporting system should be reviewed, and necessar}^ changes made to adapt the system for accumulating relevant data. This would necessitate a proper classification between direct and indirect labor, and a separate collection of data on labor elements which are subject to abnormal fluctuations, such as inspection. 2. Arrangements should be made to collect inform.ation on suboperations, or even sub-sub-operations. The costs of detailed collections would have to be balanced by the added accuracy of reported figures for purposes of decision-making. 3. Assembly and other operations should be differentiated. In the case of machining parts, details on economic lot sizes, lead time, and other pertinent information should be gathered.

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265 4. The product and the production process should be studied. It should be ascertained whether the product or a similar variety was produced before, and the degree to which any transfer of experience could have taken place should be ascertained. 5. The unit of production should be properly defined. 6. Historical data on the product and the production process should be collected. The importance of this procedure may not be evidenced in the beginning, but would be of considerable help as production continues . 7. Only actual figures obtained in the normal process of production should be used for initial analyses. As far as possible, estimated amounts, such as data on prototypes, should be carefully distinguished. 8. It would be preferable to use direct labor hours, broken down by types of operations and sub-operations rather than direct labor costs. 9. If total costs are to be used as variables, it would be preferable to locate separate costs for material, labor, and overhead, and then to aggregate these at each unit of production. 10. Cost of material should be segregated from sub-contract costs and/or sub-contract hours should be separated from direct labor hours expanded in the plant. 11. The first-in first-out principle should be applied while costing sub-assemblies, machined parts, etc., in preferance to the "average" concept.

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266 12. The criterion of consistency in the process of data accumulation should be strongly adhered to. If variations arise, as they normally would in the course of production, the effects of such changes should be careflly analyzed. 13. If substantial changes are noted, the original data should be replaced by considering the product as a new one. Whether a change is "substantial" would have to depend on the accountant's judgement, or on the opinions of specialists, such as the industrial engineer. 14. Extensive qualitative information should be supplied along with the quantitative to give the decision-maker all relevant information. 15. The model that best describes the situation at hand should be used after careful and detailed observations. It is not necessary that a linear pattern emerge in every case. If some other form could fit the set of data, such form should be used. However, if a linear approximation is found to be appropriate, analysis would prove easier by use of that form. 16. Statistical tools, such as the line of best-fit by means of least-square computations, orthogonal polynomials and the standard error of estimate should be utilized to determine the form and influence of experience. 17. Periodic evaluation should be conducted to determine the efficacy of the relationship as a tool for planning and control. If a particular model is used, the applicability of that model should be checked whenever possible.

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267 18. Some form of continuous or periodic reporting should be introduced. The exact form of reporting would have to depend upon the particular circumstances, however, some form of dynamic data reporting to higher management should be undertaken. Reporting by the principle of exception could prove economical and effective. 19. Proper controls should be maintained to check the accuracy and reliability^ of data. A periodic audit should be undertaken to ascertain the accuracy and reliability of data generated. A seldom-analyzed characteristic was researched in detail in order to unearth important implications. It has been x^idely recognized that the linear logarithmic function can rarely be a smooth straight line. Hence, some form of a smoothing process has to be undertaken to derive a smooth projection. Statistical tools have to be used to draw such a function, and it was regarding the usage of statistical tools and mathematical concepts that a lack of understanding was evidenced and, hence researched by this study. It was noted that any form of a function could be fitted by eye to any set of production data; however, such a fit may not be the best fit. Dynamic production data, when plotted, result in a scatter diagrar even on logarithmic grid graph paper. This scatter may be best represented by a linear function; however, one cannot assert this without testing the fit. Statistical methods are available by which the degree of significance for different degree curves can be tested, and unless such tests are applied, one cannot assert that a particular fit is better than another. Moreover, it is generally accepted that dynamic

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268 data can be best represented on logarithmic grid graph paper. The relative changes emphasized by the logarithmic scale appear to be more advisable than the plain graph rectangular grids. However, significantly valid reason for using this transformation instead of plain graphing for dynamic data was evidenced. Data from an actual production situation were utilized to illustrate some of the observations. It was concluded that all dynamic data should first be plotted on plain graph paper and the trend noted. A "smooth" trend does not appear to be necessary; merely connecting the plot-points may be all that is required. However, if smoothing is to be undertaken, the significance of different degree functions should be tested for their fit by means of the orthogonal polynomial computations. The data should then be plotted on logarithmic grid graph paper, and the trends tested. For short-run planning forecasts, plain graph paper could prove as valuable as logarithmic paper. Long-run forecasts should be avoided as far as possible for the danger of enlarged errors would be proportionate to the degree of extrapolation achieved. However, if the important variables could be quantified, the logarithmic graph may prove more usable than the arithmetic grids, but only for forecasting. For control purposes, arithmetic graph paper appears to be more helpful than the logarithmic graph paper at all levels of production. The use of orthogonal polynomials for testing fits and deriving trends v;as commented on, along with the method of least-square fits for linear trends. In connection with trend fitting, it was observed that the number of units used while determining a trend could significantly

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269 influence the shape and slope of the resultant function. This implies that extreme care would have to be taken to ascertain whether the conditions and assumptions used while analyzing the initial data remain the same for later production, otherwise the extrapolated values would be liable to serious error. Moreover, constant checks, including statistical tests, should be conducted to determine the reliability of the smoothened trend. Past, present, and forecasted future information connected with the product and the production process should be carefully analyzed as frequently as possible. It v7as also noted that the cumulative average function was more stable than the unit hour curve. A greater degree of dispersion between the plotted values results from plotting unit hours; however, the process of averaging leads to a smoother cumulative average function. Hence, the cumulative average curve would be better suited for planning purposes; on the other hand, the unit hour plot could be profitably applied for control purposes for it emphasizes discrepancies and indicates the magnitude of variations. After a short comment on the meaning of the experience rate, it was pointed out that this rate is different from the slope of the curve. The significance of the experience rate as an indicator of production efficiency was investigated, and it was concluded that although the experience rate can signify efficiency, such a judgement cannot be made without a detailed investigation, for the rate can be influenced by preproduction planning as well as during-production factors. Pre-production planning affects the cost of the first unit and the resultant experience rate. Thus, a higher degree of such planning would normally lead to a

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270 lower cost for the first unit and a higher experience rate than where such planning was not undertaken. Hence, a smaller experience rate without proper pre-production planning may not be more efficient than a flatter curve for a well-planned product. A tentative hypothesis was then stated: that properly planned products would tend to have flatter but more stable functions, and hence would be more reliable as bases for planning. Due to the above implications, it was considered advisable to analyze the factors that could affect experience rates, by differentiating between pre-production and during production influences, on the expectation that this dichotomj' would provide a fruitful basis for analysis. Among the pre-production factors, the anticipated rate of output and estimated volume of production V7ere pointed out as two important determinants of the experience rate. Pre-production planning would be considerably influenced by these two factors, along with planning for capacity, tools, engineering specifications, work-methods, materials, m.aterial suppliers, sub-contractors, personnel acquisition, shop organization, and overall coordination. Although a separate list of during-production factors was attempted, it was recognized that the pre-production factors would partially control the impact of duringproduction influences. The during-production factors which could affect the rate of improvement were then listed, and it was argued that the introduction of the human factor through direct labor would be a significant determinant of the experience rate. Thus a higher manualmechanical ratio for operations would result in a smaller experience

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271 rate than one where operations were predominantly mechanized. Several other factors were also recognized, chief among which were more efficient supervision; improvement in tooling; faster inspection procedures; more knowledgeable managerial decisions and policies; improved clerical, personnel, and other administrative services; time-saving engineering and design modifications; improvement in production methods and processes, in industrial engineering aids, in material procurement and handling, and in the general state of knowledge; more efficient combination of resources; and, above all, a better balanced organic coordination. Finally, specific implications for managerial accounting, in its function of reporting costs and aiding management in decisions regarding planning and control, were investigated. It was noted that the factor of experience could affect costs, and hence, whenever possible, effort should be made to incorporate the factor in conventional analyses. It was asserted that the results of this study did not invalidate or refute any conventional procedures or concepts, but merely indicated that a refinement could be achieved by introducing the factor of experience as an additional variable. It was noted that experience could affect the cost of materials and actual overhead, although not as noticeably as it could affect the direct labor element. Material control procedures could be improved and conventional formulae for the calculation of economic lot size, minimum order point, etc., could be made more accurate by introducing the additional variable. Applied overhead would be affected in the same manner as direct labor hours or costs (assuming the overhead rate to be based on direct labor hours or costs).

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272 Very little can be conceptualized regarding implications for actual overhead, and unless empirical studies are undertaken to observe the behavior of manufacturing overhead under continuous production conditions, no generalizations can be hypothesized. Implications for marketing costs and general administrative expenses vere also investigated, and it V7as noted that, although the scope for profitable utilization of the quantification procedures for administrative expenses was questionable, that for distribution costs appeared to be considerable. It was suggested that more research be directed toward the application of dynamic analysis for selling and distribution expenses, and the reason for this suggestion was explained. The influence of experience on unit costs was then noted, and it was asserted that absolute costs can be arrived at by ascertaining the cost of each element imbedded in a unit of product and aggregating these elements, or by estimate the aggregate cost for the anticipated volume of productuion and dividing that by the number of units. It was stated that the latter might be a m.ore acceptable means, for a rough measure of the decline in costs with increased production would be automatically taken into consideration. However, the best approach would be to plot the data and locate a trend, and to use that trend for ascertaining costs, which provides a variable cost per unit. Similar analysis was conducted for profit estimation and calcuation. If pricing was based on an average cost, the initial units produced would be sold at a loss, and perhaps no net profit would be forthcoming until a substantial number of units were produced and sold. Implications for inventory

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273 forecasting and valuation were also found to be affected by the quantity produced. Perhaps the most important implication discussed in the section on costing was the impact on break-even analysis and other tools and techniques where the fixed cost-variable cost dichotomy has been accepted. The assumption that variable cost would be constant per unit of production has been generally accepted for accounting analyses. This study has strongly opposed the assumption for it was seen that the variable cost per unit would decline with increased production and hence, using a constant variable cost per unit might tend to give unreliable results. Tnis failing was illustrated on the break-even analysis, and a significant variation was noted between the conventional breakeven point and the refined break-even point. It became evident that direct costing procedures could be significantly affected, and if the effects of experience are to be considered, additional calculations would be involved. Implications for planning were also noted. It was suggested that the cumulative average plots be used, and preferably only shortterm forecasts be made, unless distant variables could be quantified. It was noted that the experience factor could be quantified for better labor requirement forecasts, production scheduling and plant utilization. The subject of pricing needed special attention, for ethical as well as legal conditior ,'ere involved. In the case of complex production it was found conceivable that a monopolistic power could

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be assumed by an initial producer, and, therefore, he could regulate future prices. Similar analysis was applied to purchasing and subcontracting. A possible reason for the failure of individual and group wage incentive schemes was indicated. Since most incentive schemes use absolute standards they were found to be inherently unstable. It was suggested that some form of a sliding-scale standard be used as an effective incentive. Budgeting for cash, funds, and capital equipment could also be refined by considering the effect of experience on the quantity produced, especially where huge and complex products are produced. Finally, implications for special decision-making situations were viewed. Included in the analyses were make-or-buy, operate-or-lease , assemble-or-subcontract, and process-or-sell decisions; also, choosing between product lines and expansion, continuation, or contraction decisions were discussed. I"Jhile analyzing the implication for control, it was observed that dynamic data held considerable potential for refining existing control procedures. Control charts could be adapted to visualize efficiency of operation in a more meaningful manner by the use of declining projections instead of conventional mean-standards. It was observed that unfavorable trends indicated by conventional charts might not be unfavorable, and vice versa. It was asserted that the principle of management by exception along with the use of declining projections and confidence limits, could provide management with a badly needed tool for control of productive efficiency and costs. The use of standard costing and variance analysis as an important

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275 managerial accounting tool for control was next analyzed, and it was concluded that the use of absolute values as standards could prove unreliable. Unfavorable variances at the initial stages of production under conventional standard costing might actually be favorable variances, and vice versa. It was suggested that where the impact of experience was ascertained to be negligible, conventional procedures could be applied, with more frequent revisions if necessary. However, in the production of time-consuming and complex products some form of a sliding scale standard should be used, or variance analysis should be adjusted to take into consideration the level of production. The study ended with an examination of the use of dynamic data in the measurement of a few other aspects, including design changes, worker potential, supervisory and managerial capability, and cost reduction programs. In conclusion it may be reiterated that the implications of repetitive operations should be taken into consideration as a possible variable in managerial accounting analyses. Dynamic data can be accumulated and utilized for more efficient planning and control, and the procedure for quantification is no more troublesome than any other aid used for facilitating managerial decision-making. The study of dynamic data should not be constrained by the experience curve "theory" specifications. Each product or firm should be treated as an organic entity and the principle of relevancy should be applied for determining trends and other bases for analyses. Above all, it should be remembered that the experience factor can be quantified and profitably utilized. During the course of research for this study, a need for more

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276 einpir^cal and conceptual investigations into specific areas was noted. Most of the problems requiring further study were pointed out in the text, and hence only a few significant topics have been selected for special mention. It is hoped that the following list will aid future research on the subject: 1. Implications for economic theory holds considerable scope for investigation. It is conceivable that some form of a microdynamic analysis could be initiated. 2. Factors affecting experience, and how these could be controlled for raising overall efficiency is another area with considerable research potential. A team effort utilizing an interdisciplinary approach could prove far more valuable than an individual's attempt at "listing" factors. It is hoped that such an attempt will be undertaken in the future. 3. Dynamic trends in specific industries could also prove valuable. Airframe manufactures serves as an excellent example of an industry where observed trends were easily adapted by several firms within the group. 4. There is a distinct lack of empirical research in the use of dynamic production data as a tool for managerial control, opening up an avenue for investigation. 5. A similar lack of analx'sis ,and hence potential for research, can be evidenced for selling and distribution accounting. 6. Finally, systems for accumulating and classifying accounting data, including classification by cost elements, and the use of electronic data processing, present considerable scope for research.

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APPENDICES

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APPENDIX A OTHER TERMS USED IN PLACE OF, OR IN REFERENCE TO, THE EXPERIENCE CURVE The "Experience Curve" concept has been referred to by several names, and it is interesting to note the varied references. Sonie of the terms mentioned below are more descriptive of the concept than others but no attempt has been mace to analyze or comment on the suitability of any. A few references are distinctly misrepresentative, or have been wrongly utilized in literature on the subject due to misconceptions. However, these have also been mentioned, along with minor variations, to indicate possible usage by works on the subject. No attempt has been made to give credit to individual authors, for a majority of the terms received their "names" under practical situations, and the risk of awarding false credit appears to be extremely high. Some of the terms used are: 1. Learning Curve 2. Progress Curve 3. Manufacturing Progress Function 4. Manufacturing Scale Function 5. Performance Curve 6. PerformanceImprovement Curve "For details on these aspects refer to: Y. Bhada: "The Experience Curve (Unpublished Miaster's Thesis, Bowling Green State University, 1965). 278

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279 7. Percent Improvement Curve 8. Improvement Curve 9. Labor-Improvement Curve 10. Direct-Labor Time-Reduction Curve 11. Time-Reduction Curve 12. Eighty Percent Curve 13. Dynamic Cost Function 14. Cost Curve 15. Cost-Quantity Relationship 16. Production Time-Quantity Relationship 17. Natural Productivity Increase Function 18. Growth Curve 19. Efficiency Curve 20. Production-Acceleration Curve.

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APPENDIX B UNIT HOUR FORMULA MODIFIED FOR DESIGN CHANGES AS SUGGESTED BY GARG AND MILLIMAN'V Y. = ^f 2^-1 J (H-b)n DJ i = 1 Oi 1 (Parameters Y , b, and n may be estimated from actual experience if a program is in progress.) Key: n = negative exponent of the slope Y. = unit man-hours for the jth version "^£ = unit man-hours for the first plane b = equivalent units of experience available at the start of the manufacturing program D-' = total number of drawings for the jth version n = number of versions in the product family D. = number of drawings for the ith work group Xi = number of units of experience for work category i. A. Garg and P. Milliman, "Tlie Aircraft Progress Curve Modified for Design Changes," The Journal of Aeronautical Engineering , XII, (January February, 1961), pp. 23-28. ^ 280

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APPENDIX C DERIVING THE LOGARITHMIC LINE OF BEST FIT USING THE METHOD OF LEAST SQUARES The least squares analysis involves the use of two simultaneous equations which have to be solved, in order to determine the values to be used for the Y-intercept and the slope of the line. Since the straight line to be derived is for logarithmic grids, the following exposition has been adapted for logarithmic calculations .'' The two equations are: Y' = na' + b X' X'Y' = a' X' = b (X') where Y' is the sum of the logarithmic values of the number of hours (unit or cumulative average), X' is the sum of the logarithmic values of the number of units, n represents the number of plot points, a' is the logarithmic value of the Y-intercept, i.e., the value of log Y when X = 1, b is the exponent of the slope. Table C-I is an extract of the manual calcuations involved. The values for X and Y have been taken from Tables IV-I and IV-II. Substituting the values in the above equations, we get: 162.443683 = 44 a' + 54.434601 b 206.362664 = 54.434601 a' + 73.629335 b Solving the equations, we get b = -.12087, and a' = 3.84144. The 281

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282 antilog of 3.84144 z'.ves us the Y-intercept, 6,941 hours approximately. This gives us one plot point. To get the other plot point the equation log Y = log a + b log X can be used, for the values of a and be are now known, and some values for X can be substituted. Thus, for X = 10, we can get: Log Y = 3.84144 .12087 (log 10) = 3.84144 .12087 (1) : = 3.72057 Y = antilog of 3.72057 = 5,255 hours. Tnus , a second point can be plotted for X = 10, Y = 5,255, and a straight line drav/n through these two points. The linear function AB in Figure IV-7 is the result of the above calculations. All other lines of best fit using the least square method indicated in Chapter IV were arrived at using identical calculations. A similar approach has been illustrated by A. E. Burrow, "Use of Learning Curves in Contract Audits," The GAG Review (Winter, 196 7), p. 38.

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283

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BIBLIOGRAPHY Books Batty, J. Standard Costing . London: Macdonald and Evans, Ltd., 1960. Berghell, A. B. Production Engineering in the Aircraft Industry . New York: McGraw-Hill Book Company, Inc., 1944. Croxton, F. E. , and Cowden, D. J. Applied General Statistics . 2nd ed. Englewood Cliffs, New Jersey: Prentice-Kail, Inc., 1955. Danielsson, Albert. On Measurement and Analysis of Standard Costs . Stockholm: Tne Business Research Institute, Stockholm School of Economics, 1963. Deinzer, Harvey T. Development of Accounting Thought . New York: Holt, Rinehart and Winston, Inc., 1965. Edwards, Allen L. Statistical Methods for the Behavioral Sciences . New York: Holt, Rinahart and Winston, Inc., 1964. Falk, Stephen Ackley. Improvement Curve Analysis Techniques . Boston, Massachusetts: Harbridge House, Inc., 1959. Fisher, Ronald A. Statistical Methods for Research Workers . 13th ed. New York: Hafner Publishing Company, Inc. , 1953. Gillespie, Cecil. Standard and Direct Costing . Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1962. Henrici, Stanley B. Standard Costs for Manufacturing . 3rd ed. New York: McGraw-Hill Book Company, Inc., 1960. Herrick, Virgil E. , and Kerbovig, Marcella. Using Experience Charts with Children . Columbus, Ohio: Charles E. Merrill Books, Inc., 1964. Hilgard, Ernest R. , and Bower, Gordon H. Theories of Learning . 3rd ed. New York: Appleton-Century-Crof ts , 1966. Keachie, E. C. Manufacturing Cost Reduction Through the Curve of Natural Productivity Increase . Berkeley, California: Institute of Business and Economic Research, University of California, 1964. 284

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285 Levi, Albert William. Varities of Experience . New York: The Ronald Press Company, 1957. McGeoch, John A., and Irion, Arthur L. The Psychology of Human Learning . New York: David McKay Company, Inc., 1961. Moore, C. L. , and Jaedicke, R. K. Managerial Accounting . 2nd ed . Dallas, Texas: Sou th-Wes tern Publishing Co., 196 7. Neter, John, and Wasserman, William. Fundamental Statistics for Business and Economics . 3rd ed. Boston: Allyn and Bacon, Inc., 1966. Reguero, Miguel Angel. An Economic Study of the Military Airframe Industry. Dayton, Ohio: Air Materiel Command, Wright-Patterson Air Force Base, 1957. Snedecor, George W. Statistical Methods . 5th ed. Iowa City, Iowa: -The Iowa State University Press, 1956. Wallis, W. A., and Roberts, H. V. Statistics: A New Approach . Brooklyn, New York: Tne Free Press of Glencoe, Inc., 1956. Articles Alchian, Armen A. "Costs and Outputs," The Allocation of Economic Resources . M. Abramovitz, et al . Stanford, California : Stanford University Press, 1959. "The Analysis of Manufacturing Cost Variances," N. A. C. A. Bulletin . XXXII, Sec. 2 (August, 1952), 1547-82 Andress, Frank J. "The Learning Curve as a Production Tool," Harvard Business Review , XXXII (January-Februarj' , 1954), 87-88. Ashby, W. R. "The Effect of Experience on a Determinate Dynamic System.," Behavioral Science , I (January, 1956), 35-42, Barron, L. A. "Learner Curves Boost Team Output," American Mechanist, CII (December 1, 195S), 100-101. Bellov/s, Roger. "The Management of Learning: I. Tneory and Practice," Personnel Administration , XXIII (January-February, I960), 21-28. Bellows, Roger. "The Management of Learning: II. Efficiency and Economy," Personnel Administration , XXIII (March-April, I960), 4-10.

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286 Bellows, Roger., and Bellovzs , Carol. "The Management of Learning: III. We Lay Waste our Powers," Personnel Administration, XXIII (November-December, 1960), 19-26. Billon, S. A. "Industrial Learning Curves and Forecasting," ManagementInternational Review , No. VI (1966), 65-79. Blair, Carl. "A Primer on Learning Curves," Factory (April , 1966) , 80-81 Boren, William H. "Some Applications of the Learning Curve to Government Contracts," N. A. A. Bulletin , XLVI, Sec. 1 (October, 1964), 21-22. Bowers, W. Bert. "Who's Afraid of the Learning Curve?" Purchasing , LX (March 24, 1966), 77-79. Brenneck, Ronald. "B E Charts Reflecting Learning," N. A. A. Bulletin XL, Sec. 1 (June, 1959), 34. Brenneck, Ronald. "The Learning Curve for Labor Hours For Pricing," N. A. A. Bulletin , XXXIX, Sec. 1 (June, 1958). 77-78. Brenneck, Ronald. "Learning Curve Techniques for More Profitable Contracts," N. A. A. Bulletin , XL, Sec. 1 (July, 1959), 59-69. Brewer, Delbert L. "The Use of Graphs in Audit Reports," The U. S. Army Audit Agency Bulletin (March, 1964), 54-59. Bryan, Stanley E. "Fair Value and the Learning Curve," Purchasing , KiXVII (September, 1954), 95-100. Burchard, Joseph R. "A Critical Look at the Marginal Graph Technique," N. A. A. Bulletin , XLII, Sec. 1 (May, 1961), 25-32. Burrow, Arnett E. "Use of Learning Curves in Contract Audits," The GAP Review (Winter, 1967), 35-46. Cangelosi, Vincent E. , and Dill, William R. , "Organizational Learning: Observations Toward a Theory," Administrative Science Quarterly , X (September, 1965), 175-203. Canova, Joseph. "Two Ways to Use the Learning Curve," Purchasing , LXIII (March 25, 1965), 80-83. Carr, Gardner W. "Peacetime Cost Estimating Requires New Learning Curves," Aviation (April, 1946), 76-77. Chamberlain, E. H. "Proportionality, Divisibility, and Economics of Scale," Tne Quarterly Journal of Economics ,LXII (February, 1948) 229-62.

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287 Chassan, Jack. "Estimating Direct Labor Costs in Aircraft Production," Industrial Aviation , III (July, 1945), 56-62. Chenery, Hollis B. "Engineering Production Function," The Quarterly Journal of Economics , LXIII (November, 1949), 507-31. Cochran, E. B. "New Concepts of the Learning Curve," The Journal of Industrial Engineering , XI (July-August, 1960), 317-27. Cole, Reno R. "Got a New Product Idea?" American Machinist , IX (December 5, 1955), 121-26. Cole, Reno R. "Increasing Utilization of the Cost-Quantity Relationship in Manufacturing," The Journal of Industrial Engineering , LXIII (May-June, 1958), 173-77. Conway, R. W. , and Schultz, Andrew. "The Manufacturing Progress Function, The Journal of Industrial Engineering , X (January-February, 1959), 39-54. Crawford, James R. "Statistical Accounting Procedures in Aircraft Production," Aero Digest , XLIV (March 15, 1944), 78-81. Grouse, P. B. "Projecting Labor Loads in Aircraft Production," Aero Digest , XLIII (October, 1943), 216-18 and 242-43. Davis, Louise E. "Toward a Theory of Job Design," The Journal of Industrial Engineering , VIII (September-October, 1957), 305-09. DeJong, J. F. "The Effects of Increasing Skill on Cycle Time and Its Consequences; for Time Standards ," Ergonomics, I (November, 1957); 51-60. Eisemann, Doris M. "The Progress -Curve Computer," Operations Re search, (January -February, 1959), 128-30. Eitington, Julius E. "Experience -As the Wags (and others) See It," Personnel Administration , XXV (November-December , 1962) , 54-56. Garg, Anand, and Milliman, Pierce. "The Aircraft Progress Curve Modified for Design Changes," The Journal of Aeronautical Engineering , XII (January-February, 1961), 23-28. Gawa, John. "Learning Curves and the Auditor," The U. S. Army Audit Agency Bulletin (March, 1964), 60-62. Ghormley, Glen E. "The Learning Curve: I," Western Industry (September, 1952), 31-34. Ghormley, Glen E. "The Learning Curve: II," Western Industry (October, 1952), 37-39.

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288 Ghorraley, Glen E. "The Learning Curve: III, Fitting the Worker to the Job," Western Industry (December, 1952), 47-49. Ghormley, Glen E. "The Learning Curve: IV," Western Industry (February 1953), 61-65. "" Giannini, Gabriel M. "Aircraft Cost Control," Aero Digest , XXXIX (August, 1941), 187-89. Hadley, J. R. "Learning Curves on Log-Log Paper," Advanced Management , XV (April, 1950), 16-17. Hall, Lowell H. "Experience with Experience Curves for Aircraft Design Changes," N. A. A. Bulletin , XXXIX, Sec. L (December, 1957), 59-66. Hartley, K. "The Learning Curve and its Application to the Aircraft Industry," Journal of Industrial Economics , XIII (March, 1965), 122-28. Heuser, Forrest L. "You Can Control Starting Costs," K. A. C. A. Bulletin , XXX\'III, Sec. 1 (April, 1957), 1047-52. Hirsch, Werner Z. "Firm Progress Ratios," Econometrica , XXIV (April, 1956) 136-43. Hirsch, Werner Z. "Manufacturing Progress Functions," The Review of ' Economics and Statistics , XXXIV (May, 195 2), 143-55. Hirsch, Werner Z. "Progress Functions of Machine Tool Manufacturing," Econometrica , XX (January, 1952), 81-82. Hirschmann, Winfred B. "Profit from the Learning Curve," Harvard Business Review , XLII (January-February, 1964), 125-39. Hirshleifer, Jack. "The Firm's Cost Function: A Successful Reconstruction," rne Journal of Business ,XXXV (July, 1962), 235-55. Jordan, Raymond B. "Learning How to Use the Learning Curve," N . A . A . Bulletin , XXXIX, Sec. 1 (January, 1958), 27-39. Jordan, Raymond B. "What's Your Progress Curve?" N. A. A. Bulletin , XLIII, Sec. 1 (March, 1962), 91-92. Keachie, E. C. "Cost and the Learning Curve," AACE Bulletin . Ill (June, 1961), 32-34. Keachie, E. C, and Fontana, R. J. "Effects of Learning on Optimal Lot Size," Management Science , Series B, XIII (October, 1966), 102-8.

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289 Kilbridge, M. D. "Predetermined Learning Curves for Clerical Operations,' The Journal of Industrial Engineering , X (May-June, 1959), 203-9. Knowles, A. R. , and Bell, L. F. "Learning Curves Can Save You Time and Money," Factory Management and Maintenanc e. CVIII (June 1950) 115. ' Koen, Francis T. "Dynamic Evaluation," Factory , CXVII (September 1959) 99-103. Kottler, Julian L. "The Learning Curve -A Case History in its Application," The Journal of Industrial Engineering . XV (Julv -August 1964), 176-80. Laddon, I. M. "Reduction of Man-Hours in Aircraft Production," Aviation XLII (May, 1943), 170-73 and 356-60. Lappin, Royal E. "Engineers and Cost Accountants -A Comment," N. A. A. Bulletin , XLIII, Sec. 1 (August, 1962), 93-94. "The Learning Curve Short Cut to Cost Reduction," Purchasin g XLV (September 29, 1958), 80-83. Lundberg, Robert H. "Learning Curve Theory," SAE Journal LXIV (May 1956), 48-49. ' McCampbell, E. W. , and McQueen, C. W. "Cost Estimating from the Learning Curve," Aero Digest . LVI (October, 1956), 36-39. Mensforth, Eric. "Airframe Production Part I," Aircraft Produ ction IX (SeptemberJ947), 388-95. "' Mensforth, Eric. "Airframe Production Part II," Aircraft P roduction IX (October,1947), 343-50. ' Metaxas, Ted. "Case Study in Modern Purchasing How Aero Uses the Learning Curve," Purchasing , LI (September 25, 1961), 79-80. Metz, Philip B. "A Manufacturing Progress Function Nomograph," The Journal of Industrial Engineering. XIII (July-August, 1962), 253-56. Middleton, Kenneth A. "Wartime Productivity Changes . in the Airframe Industry," Monthly Labor Review . LXI (August, 1945), 215-225. Neal, Dewey W. "Straight-Line Projections with the Learning Curves " N. A. A. Bulletin. XLII, Sec. I (June, 1961), 62. Nielson, Oswald, "Learning Curves in Construction," Accountant s' Cost ISHdbook, 2d ed., R. I. Dickey (cd.). New York: The l-lonald Press Company, 1960, 23-25.

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290 Noyes, C. Reinold. "Certain Probleins in the Empirical Study of Costs," The American Economic Review , XXXI (September, 1941), 473-92. Pooler, Victor H. , Jr. "How to Use the Learning Curve," Purchasing , LI (July 17, 1961), 70-73. Powers, Frank J. "Costs Strike Out v;ith Learning Curve Incentive," Factory (October, 1961), 90-91. Preston, L. E. , and Keachie, E. C. "Cost Functions and Progress Functions," The American Economic Review, LIV, Part I (March, 1964), 100-107. Rayborg, W. A., Jr. "Mechanics of the Learning Curve," Aero Digest , UN (November, 1952), 17-21. Robbins , Sidney M. , and Murphy, Thomas E. "Economics of Scheduling for Industrial Mobilization," The Journal of Political Economy , LVIII (February, 1949), 30-45. Rigdon, C. J. "Analysis of Progress Trends in Aircraft Production," Aero Digest , XCV (May 15, 1944) 132-37. Ruggles , Richard. "Tae Concept of Linear Total Cost Output Regressions," The American Economic Review , XXXI (June, 1941), 332-35. Sanders, B. T. , and Blystone, E. E. "The Progress Curve -An Aid to Decision-Making," N. A. A. Bulletin . XLII, Sec. 1 (Julv, 1961), Sl-86. Sandler, Irving J. "Dial for Computer Audit Assistance," The Federal Accountant , XVI (Fall, 1966), 15. Schneider, Lester J. "Calculating Price Determining Factors -A Procedure," N. A. A. Bulletin , XLIII, Sec. 1 (December, 1961), 83-88. Searle, Allan D. "Productivity Changes in Selected Wartime Shipbuilding Programs," Monthly Labor Review , LXI (December, 1945), 11321147. Shroad, Vincent J., Jr. "Control of Labor Costs Through the Use of Learning Curves," N. A. A. Bulletin, XLVI, Sec. L (October, 1964). 15-20. Siersema, John N. "The Learning Curve," Cost and Management (May, 1960). 186-200. Smith, Spencer B. "The Learning Curve: Basic Purchasing Tool," Purchasing , LVIII (March 11, 1965), 70-75.

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291 Smith, Wayland P. "An Investigation of Some Quantitative Relationships Between Break-Even Point Analysis and Economic Lot Size rneory," Tne Journal of Industrial Engineering , IX (January -Feb ruary , 1958), 52-57. Taylor, Marvin L. "The Learning Curve -A Basic Cost Projection Tool," K. A. A. Bulletin , XLII, Sec. 1 (February, 1961), 21-6. Titleman, Morton S. "Learning Curves -Key to Better Labor Estimates," Product Engineering , XXVIII (November 18, 195 7), 36-38. Wertman, Lou. "Putting Learning Curves to Work," The Tool Engineer , XLIII (September, 1959), 99-102. White, James M. "The Use of Learning Cur\re Theory in Setting Management Goals," The Journal of Industrial Engineering , XII (NovemberDecember, 1961), 409-411. Wilkerson, William F. "Application of Learning Curve Techniques to Audit," The U. S. Army Audit Agency Bulletin (June, 1964), 47-50. Williams, J. A. C. "Learning Curves in Production Planning," Time and Motion Study , VI (May, 1957), 18-23. Williams, Paul F. "The Application of Manufacturing Improvement Curves in Multi-Product Industries," The Journal of Industrial Engineering , XII (March-April, 1961), 108-112. Wood, Marshall K. "Representation in a Linear Model of Nonlinear Growth Curves in the Aircraft Industry," Activity Analysis of Production and Allocation , T. C. Koopman (ed.) New York: John Wiley & Sons, Inc. , 1951. Wright, T. P. "Aviation's Place in Civilization," The Journal of the Royal Aeronautical Society, XVIX (1945), 299-340. Wright, T. P. "Factors Affecting the Cost of Airplanes," Journal of the Aeronautical Sciences , III (Februarys 1936), 122-128. Wyer, Rolfe "Industrial Accounting with the Learning Curve," The California C.P.A. , XXIII (February, 1957), 24-30. Wyer, Rolfe "Learning Curve Helps Figure Profits, Control Costs," N. A. C. A. Bulletin , XXXV, Sec. 1 (December, 1953), 490-502. Wyer, Rolfe. "Learning Curve Techniques for Direct Labor Management," N. A. A. Bulletin , XXXIX, Sec. II (July, 1958), 19-27. Wylie, K. H. ,and Ezekiel, M. "The Cost Curve for Steel Production," The Journal of Political Economy , XLVIII (December, 1940) ,' 777-821 .

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292 Other Publications Alchian, Armen A. An Airframe Production Function . P-108, Santa Monica, California: The Pvand Corporation, October 20, 1949. Alchian, Armen A. Reliability of Progress Curves in Airframe Production . RM-260-1, Santa Monica, California: The Rand Corporation, February 3, 1950. Arrow, Kenneth J., and Arrow, S. Methodological Problems in Airframe Cost Performance Studies . R14-456, Santa Monica, California: The Rand Corporation, September 20, 1950. Arrow, Kenneth J., Arrow, S., and Bradley, H. Cost-Quality Relations in Bomber Airplanes . R>I-536, Santa Monica, California: The Rand Corporation, February 6, 1951. Asher, Harold. Cost-Quantity Relationships in the Airframe Industry , R-291, Santa Monica, California: The Rand Corporation, Julv 1, 1956. Barnes, Ralph M. , Perkins, James S., and Juran, J. M. "A Study of the Effects of Practice on the Elements of a Factory Operation," University of Iowa Studies in Engineering. Bulletin 22 (November, 1940). Crawford, James R. , and Strauss, Edwin B. Cravzford-Strauss Study . Air Materiel Command, Wright-Patterson Air Force Base, Dayton, Ohio, 1947. Development of Production Acceleration Curves for Airframes . Stanford, California: Stanford Research Institute, September, 1948. Directorate of Procurement and Production, Alpha and Omega and the Experience Curve , U. S. Army Missile Command, Redstone Arsenal, Alabama, April 12, 1965. Guibert, P. Mathematical Studies of Aircraft Construction . WrightPatterson Air Force Base, Dayton, Ohio, 1945. Hoffman , S. Fred. Comments on the Modified Form of the Aircraft Progress Function , RI-4-464, Santa Monica, California: The Rand Corporation, October 4, 1950. Krocker, Herbert R. , and Peterson, Robert. A Handbook of Learning Curve Techniques . The Ohio State University Research Foundation, 1961. National Aeronautics and Space Administration, Guidelines for Evaluation of Contractor Accounting Systems , NHB 9090.6, February, 196 7 Edition.

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293 National Aeronautics and Space Administration, Procedures for Reporting Cost Information from Contractors , KHB 9501.2, March, 1967 edition. Novick, David. Use of the Learning Curve , P-267, Santa Monica, California: The Rand Corporation, November 9, 1951. Relationships for Determining the Optimum Expansibility of the Elements of a Peacetime Aircraft Procurement Program . Stanford, California: Stanford Research Institute, December, 1949. Unpublished Baloff, Nicholas. "The Manufacturing Progress Model: A New Application, Unpublished Master's thesis, Massachusetts Institute of Technology, 1960. Bhada, Y. K. "The Experience Curve," Unpublished Master's thesis. Bowling Green State University, August, 1965. Billon, S. Alexander. "Industrial Time Reduction Curves as Tools for Forecasting," Unpublished Doctoral dissertation, Michigan State University, 1960. Buccini, George Eugene. "The Learning Curve as a Direct Labor Tool in the Aircraft Industry," Unpublished Master's thesis, Southern Methodist University, June, 1958. Crawford, James R. "Estimating, Budgeting, and Scheduling," Lockheed Aircraft Corporation, Burbank, California, 1944. Crawford, James R. "Learning Curve, Ship Curve, Ratios, Related Data," Lockheed Aircraft Corporation, Burbank, California, n.d. Fowlkes , Tommie F. "Aircraft Cost Curves: Derivation, Analysis, Projection," CRA-64-1, General Dynamics, Fort Worth, Texas, August, 1963 (re-issue). Hammer, Kenneth Fredrick. "An Analytical Study of Learning Curves as a Means of Relating Labor Requirements to Production Quantities," Unpublished Master's thesis, Cornell University, September, 1954. Hoffmann, L. C, and Tangerini , C. C. "Reducing Costs of American Ships. A paper presented at the Annual Meeting of the Society of Naval Architects and Marine Engineers, New York: November, 1961. 'Improvement Curve Analysis Techniques," Defense Contract Audit Manual , Appendix F. July, 1965. Link, Gordon W. , and Ellis, Don A. "The Experience Curve as Used by the Cost Accounting Department," Boeing Aircraft Company, Wichita, Kansas, December, 1945.

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Maynard, B I. "Mathematical Tneory of Time Reduction Curves," Proceedings of the Fifth Annual Industrial Engineering Institute , University of California, 1953. Morgan, A. W. "Experience Curves Applicable to the Aircraft Industry," The Glenn L. Martin Company, Baltimore, Maryland, September 27, 1957. Rutan, E. A. "Tlieory of Learning Curves," Chance-Vought Aircraft, Inc., Dallas, Texas, October, 1948. Schreiner, Donald A. "The Manufacturing Progress Function: Its Application to Operations at IBM, Endicott," An unpublished paper presented on behalf of International Business Machines Corporation, n.d. Shappell, N. H. "Production Application of Time Reduction Curves," Proceedings of the Fifth Annual Industrial Engineering Institute , University of California, 1953. Thue, H. W. "Time Reduction Curves," Proceedings of the Fifth Annual Industrial Engineering Institute , University of California, 1953. Weining, E. 0. "Improvement Curve Study," Boeing Airplane Company, Wichita, Kansas, August 11, 1949. Zieke, Robert Paul. "Progress Curve Analysis in the Aerospace Industry,' Unpublished Master's thesis, Stanford University, June, 1962.

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BIOGRAPHICAL SI^TCH Yezdi Khurshed Bhada was born on August 13, 1940, in Bombay, India, the fourth child in a Zorastrian family of five children. After rccoivin;; hj.s Secondary School Ccrtiricatc from St. Mary' 8 Iliyli School (English Teaching Section), he entered the University of Bom.bay where he was awarded the degree of Bachelor of Comm.erce (Honours) in 1961. In the same year, he toured Europe as a member of a famous Indian choir. On his return from Europe he managed his father's business for a short while, and later worked for a cost consultant's firm, appearing for the Institute of Cost and Works Accountants' examination at the same time. He left India in September, 1964, on receiving a graduate assistantship from Bowling Green State University, Ohio, where, a year later he received the Master of Business Administration degree. Yezdi is married to the form.er Perviz Laskari and they have been blessed with two children, Neville and Dianna. Among his accomplishments are several scholarships, a trophy awarded to the outstanding senior student by his undergraduate college, an honorary membership to the Exchange Club of Bowling Green as an outstanding foreign student, a fellowship from the Earhart Foundation, and a Beta Alpha Psi membership. 295

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This dissertation was prepared under the direction of the chairman of the candidate's supervisory committee and has been approved by all members of that committee. It was submitted to the Dean of the College of Business Administration and to the Graduate Council, and was approved as partial fulfillment of the requirements for the degree of Doctor of Philosophy. Msrch 1968 'W' 'Jr/A4Dean, Colleae of Business Administration Dean, Graduate School Sup,ervisory Committee: •^Chairman K ii BIA \ ! i_.. %^^ U'. ^U^u^

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