Title: Some implications of the experience factor for managerial accounting
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Permanent Link: http://ufdc.ufl.edu/UF00097787/00001
 Material Information
Title: Some implications of the experience factor for managerial accounting
Alternate Title: Managerial accounting
Physical Description: viii, 295 leaves : illus. ; 28 cm.
Language: English
Creator: Bhada, Yezdi Khurshed, 1940-
Publication Date: 1968
Copyright Date: 1968
Subject: Accounting   ( lcsh )
Accounting thesis Ph. D   ( lcsh )
Dissertations, Academic -- Accounting -- UF   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis - University of Florida.
Bibliography: Bibliography: leaves 284-294.
Additional Physical Form: Also available on World Wide Web
General Note: Manuscript copy.
General Note: Vita.
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Bibliographic ID: UF00097787
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000549807
oclc - 13299780
notis - ACX4109


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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.


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

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

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

I INTRODUCTION .. . . . . ..........

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


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" .. . . ......


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.

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


THE EXPERIENCE CURVE. . . . . . . . ... 278


METHOD OF LEAST SQUARES . . . . . . . . 281

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

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



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




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



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



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



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-
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

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.
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



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 )




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

** 1931
.* 5*


"* 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
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-
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-
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-
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

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


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


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-


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.

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.

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.



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
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

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


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-


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


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


A considerable amount of research has been accomplished at two
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
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


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
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





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


a- me sa manach, and L. hton Tu Pvason num Leram ne vers~ avw -..~~ us. cmpnyhe me be Ipo 2a


0 110



a. 90


u 70

S o


Learning Period

Time in Days


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


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


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


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






S C-
0- C4


0 .0
J l o




Labor Hour 4 0
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


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 o



d Iz a

u > u 1

r Uv
Ew o

Z o

a o4u

Labor Hours Per Unit


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-


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


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,


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 0



W z



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



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


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


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


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-


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

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),

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.


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.



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


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


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


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

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