SOME IMPLICATIONS OF THE EXPERIENCE
FACTOR FOR MANAGERIAL ACCOUNTING
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
UNI3 ERSITY OF FLORI
3 1262 08552 3974
The author wishes to express his indebtedness to all those who
have assisted him in achieving his goals, including his supervisory
committee members: Dr. John 11. James, Dr. Ralph H. Blodgett, Dr.
Charles W. Fristoe, and Dr. Williard E. Stone. He is especially grate-
ful to Dr. James W. Davault, committee chairman, whose patience and
guidance were most encouraging. Gratitude must also be expressed to
Dr. Harvey E. Donley, Professor of Accounting, Bowling Green State
University, for his role in getting the author interested in the sub-
ject of this dissertation. Above all, he would like to express his
gratitude to his wonderful wife, Perviz, who preferred to sacrifice a
life of security and comfort to follow the man in whom she had faith.
Patiently has she endured years of hardship and loneliness, an accom-
plishment for which he bows his head in true respect.
Finally, he wishes to express his admiration for this wonderful
land of opportunity. God bless America, and all those who have made it
the great nation it is.
TABLE OF CONTENTS
ACKNOWLEDGMENTS . . . . . . . . . . . . .
LIST OF TABLES . . . . . . . . . . . . .
LIST OF FIGURES . . . . . . . . . . ... .
I INTRODUCTION .. . . . . ..........
Nature and Scope of the Study .. . . ......
Definitions of Key Terms .. . . . ......
Research Methodology Employed .. . . ......
Organization of the Remainder of This Study .. ..
II EXPRESSING THE DYNAMIC RELATIONSHIP BETWEEN COST OR
PRODUCTION TIME AND THE QUANTITY PRODUCED .. . ...
Purpose and Organization of the Chapter .. . ...
A Historical Sketch of Contributions to the Estab-
lishment of a Cost-Quantity Relationship ......
Development of the Linear Logarithmic Dynamic
Cost Function . . . . . . . . . .
The Learning Curve .. . . . ........
A Critique of the Conceptual Implications of
Experience Curve "Theories" .. . . ......
III PROJECTING DYNAMIC PRODUCTION DATA .. . . ....
Purpose and Organization of the Chapter .. . ...
Accumulation of Accounting Data .. . . .....
Possible Patterns in Dynamic Production Data
Variations Suggested for the Study of Dynamic Data.
IV QUANTITATIVE AND QUALITATIVE IMPLICATIONS OF THE
EXPERIENCE RATE . . . . . . . . . .
The Purpose and Organization of the Chapter .. ..
Statistical and Mathematical Implications .. ...
The Experience Rate and the Slope of the Experience
Curve . . . . . . . . . . . .
Significance of the Experience Rate .. . ....
Factors Influencing the Experience Rate .. . ...
V SPECIFIC IMPLICATIONS FOR MANAGERIAL ACCOUNTING ..
TABLE OF CONTENTS (continued)
V The Purpose and Organization of the Chapter .... 192
Implications for Costing. . . . . . . ... 193
Implications for Planning . . . . . . . 215
Implications for Control. . . . . . . ... 234
VI SUMMARY AND CONCLUSIONS .. . . . . . . 262
A OTHER TERMS USED IN PLACE OF, OR IN REFERENCE TO,
THE EXPERIENCE CURVE. . . . . . . . ... 278
B UNIT HOUR FORMULA MODIFIED FOR DESIGN CHANGES AS
SUGGESTED BY GARG AND MILLIMAN. . . . . . ... 280
C DERIVING THE LOCARITHMIC LINE OF BEST FIT USING THE
METHOD OF LEAST SQUARES . . . . . . . . 281
BIBLIOGRAPHY ............ . . . . . . ... 284
BIOGRAPHICAL SKETCH .................. . . 295
LIST OF TABLES
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
LIST OF FIGURES
I-1 Long Run Production Time Declines Experienced in
Two Industries. . . . . . . . ... .. 6
II-1 Representative "Learning Curves" As Used for Psycho-
logical Analyses ................... 49
II-2 An Actual Learning Curve Derived in a Psychological
Experiment ....... ... ............ 51
11-3 An Example of a "Learning Curve" Used for an Incentive
Wage Payment Scheme . . . . . . . .. 52
11-4 Graphical Representation of Initial Cumulative Produc-
tion Data on Arithmetic-Grids . . . . . ... 56
11-5 Graphical Representation on Arithmetic-Grids After a
Substantial Level of Production Has Been Achieved . 58
II-6 Hypothetical Data (from Table 1) Plotted on Logarith-
mic-Grid Graph Paper. . . . . . . . ... 60
11-7 Effect of Different Improvement Rates for Cost Elements
on the Total Cost Projection . . . . . . 69
II-8 Effect of Linear Component Curves of Different Slopes
on the Unit Curve . . . . . . . . ... 71
II-9 Constant Rate of Decline for Tripled Quantities As
Projected on Logarithmic-Grids. . . . . . ... 75
III-1 Constant Rate of Decline for Unit Labor Hours .... 99
III-2 Constant Rate of Decline for the Cumulative Average. 103
III-3 A "Scalloped" Representation. . . . . . . .107
III-4 Constant Rate of Decline for Lot Averages . . ... 108
III-5 A Humped Unit Hour Curve. . . . . . . 110
III-6 An "Inverted S" Curve ... . . . . . 113
III-7 Constant Rate of Decline for Equal Quantities,
Projected on Full-Logarithmic Grids . . . ... .117
LIST OF FIGURES (Continued)
III-8 Constant Rate of Decline for Equal Quantities,
Projected on Semi-Logarithmic Grids . . . ... 118
III-9 An Example of a "Leveling-Off" Curve: Lockheed,
Burbank--B 17 . . . . . . . . . 120
III-10 An Example of a "Toe-Up" Curve: Boeing Seattle,
B 17 Learning Curve . . . . . . . ... .121
III-11 An Example of a "Toe-Down" Curve: Douglas, Tulsa
B 24 Learning Curve . . . . . . . ... 123
III-12 A No-Trend Projection ..... . . . . .126
III-13 Trend-Lines from Reclassified No-Trend Data . . .. .127
IV-1 Unit Hours from Table IV-1 Plotted on Arithmetic
Grid Graph Paper .................... 144
IV-2 Unit Hours from Table IV-1 Plotted on Logarithmic Grid
Graph Paper . . . . . . . . ... . . 145
IV-3 "Raw" Trend on Logarithmic Grids. . . . . ... 146
IV-4 A Linear Function Fitted to the Data from Table IV-1. 147
IV-5 A Third Degree Polynomial Fitted to the Data from
Table IV- . . . . . . . . . . . ... 149
IV-6 Figures IV-4 Replotted with Data from Table IV-II
Added to the Original Graph . . . . . ... .152
IV-7 Straight Line Projections Using Different Points
for Derivation of Trends. . . . . . . ... 153
IV-8 Straight Line Projections Using Different Points for
Derivation of Trends, As Applied to the Cumulative
Average Plots ......... ........... .. 155
IV-9 Extrapolations of Trends Indicated in Figure IV-8
for Large Quantities. . . . . . . . ... 157
IV-10 Unit Hours from Tables IV-I and IV-II Plotted on Plain
Graph Paper with Trends Indicated Using Polynomials . 158
LIST OF FIGURES (Continued)
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
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 )
Per Unit of Output in U.S. Basic Steel Industry
500 1,000 1,500 2,000 3,000 4,000
Long Run Production Time Declines Experienced in Two Industries
'~*~""'"' """ "" """~" ~ ... ..... .. .., '~"
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
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
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-
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
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
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
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-
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
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-
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-
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-
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.
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),
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.
EXPRESSING THE DYNAMIC RELATIONSHIP BETWEEN COST OR PRODUCTION TIME
AND THE QUANTITY PRODUCED
Purpose and Organization of the Chapter
Before an investigation can be undertaken to study the derivation
and understand the implications of the experience factor for managerial
accounting, it is necessary to review and consider what has already been
done in this direction. That a relationship exists between production
time or cost and cumulative production is by no means a contribution of
this study, for a considerable amount of work has been done to support
this contention. Unfortunately, literature available on the subject,
though abundant, often appears to be over-simplified, vague, and even
contradictory, mainly due to the fact that most authors prefer to follow
the accepted "pattern," and rely on "theories" based on implied assump-
tions without a proper understanding of their implications. Most of the
information on the production time-quantity relationship is available
under the subject-title "learning curve," or "progress curve," and al-
though the subject of this research is closely connected to the "learning
curve," there is a significant difference which will be noted in the
course of this study.
The main intention of this chapter is to investigate the "learning
curve" theory as an explanation of the dynamic production time-quantity
or cost-quantity relationships as observed in industrial situations.
Does the "theory," as proposed and accepted by so many authors and prac-
titioners, really serve as a reliable representation for ordering exis-
tential and conceptual data to aid business management in its function
of decision-making? An answer to this question has been the principal
aim of the chapter.
In order to obtain an acceptable answer, it has been deemed neces-
sary to trace a short historical sketch of the "learning curve" concept,
observe its acceptance and applicability, and define its characteristics.
The different "theories" and their implied assumptions as "accepted" over
the years have been explained and critically evaluated in the course of
the chapter, keeping the managerial accountant's point of view in mind.
Particular emphasis has been placed on analyzing the "linearity assump-
tion" as a means of expressing production time-quantity relationships,
since most of the accounting literature seems to imply a universal appli-
cability for this form of representation.
This investigation is supposed to pave the way for Chapter III,
where more detailed analysis of possible production time-quantity rela-
tionships which could be profitably utilized by the managerial accountant
have been indicated.
A Historical Sketch of Contributions to the Establishment
of a Cost-Quantity Relationship
Pre-World War II experience
It was in the airframe industry that peculiarities and trends in
production time-quantity relationships were initially observed. Miguel
A. Reguero has asserted that the credit for original investigation of air-
frame production data should be bestowed upon Leslie McDill, Commanding
Officer at McCook Field (predecessor of Wright-Patterson Air Force Base,
both near Dayton, Ohio).1 Reguero's research indicated that it was
McDill's efforts in 1925 which led to the formulation of the "learning
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-
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
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
REPRESENTATIVE "LEARNING CURVES" AS USED FOR
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
AN ACTUAL LEARNING CURVE DERIVED IN
A PSYCHOLOGICAL EXPERIMENT
a- me sa manach, and L. hton Tu Pvason num Leram ne vers~ avw -..~~ us. cmpnyhe me be Ipo 2a
Time in Days
AN EXAMPLE OF A "LEARNING CURVE"
USED FOR AN INCENTIVE WAGE PAYMENT SCHEME
as elements of the same species, there are significant differences, there-
fore distinct references may be advisable.
In the opinion of this author, the term "learning curve" is best
suited for the psychologist's graphical representation, and is certainly
less descriptive of the phenomenon considered under the production time-
quantity relationship used for business decision-making. The graphical
representation used for wage incentive schemes may be appropriately re-
ferred to as the learner curve to signify its applicability to incentive
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
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
Labor Hours Per Unit
0 w N '0 a
' 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
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-
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
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
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
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
CONSTANT RATE OF DECLINE FOR TRIPLED QUANTITIES
AS PROJECTED ON LOGARITHMIC-GRIDS
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-
1. M. A. Reguero, An Economic Study of the Airframe Industry,
Air Materiel Command, Wright-Patterson Airforce Base (Dayton, Ohio:
October, 1957), p. 213.
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),
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,
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,
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.
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
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-
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),
PROJECTING DYNAMIC PRODUCTION DATA
Purpose and Organization of the Chapter
What is the role of an accountant in the proper accumulation and
dissemination of production data? How can accounting analyses concerning
an entity be undertaken so that the impact of quantity produced on costs
or production time be given adequate recognition? Partial answers to these
questions have been attempted in the next few pages.
Before any analyses can be conducted on the implications of experi-
ence gained on the quantity produced, it is essential to know how account-
ing data can be recorded, accumulated, and classified, for it is on the re-
liability of the data presented that interpretations and judgments are
based. The importance of managerial accounting depends on the accountant's
analytical judgment which, in turn, is based on his knowledge, experience,
and the reliability of data available to him. For these reasons, it is ex-
tremely important to know the proper means of accumulating data and arrang-
ing the information in a manner susceptible to adequate analysis and re-
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
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