the learninig curve historical review yelle

8/10/2019 The Learninig Curve Historical Review Yelle

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Education

TH E LEARNING CURVE: HISTORICAL REVIEW

AND

COMPREHENSIVE SURVEY

Louis E.Yelle, University

of Lowell

ABSTRACT

Th e use of the learning curve has been receiving increasing atten tion in recent years.

Much of this increase has been due to learning curve applications other than in the tradi-

tional learning curve areas. A comp rehensive survey of developments in the learning curve

area has never been published. The closest thing to a survey was by Asher in

1956.

His

study focused exclusively on military applications during and immediately after World

War 11. This paper summarizes the learning curve literature from World War

11

to the

present, emphasizing developments since the study by Asher. Particular emph asis is given

to identifying the new directions into which the learning curve has made recent inroads

and identifying fruitful areas for future research.

INTRODUCTION

The learning curve phenomenon was first reported by Wright in the litera-

ture in 1936 [89]. Th e phenomen on w hich Wright observed was tha t as the qua n-

tity

of

units manufactured doubles, the number

of

direct labor hours' it takes t o

produce an individual unit decreases at

a

uniform rate. Th e uniform rate (i.e.,

90

percent, 8 percent, 70 percent, etc.) of learning is peculiar to the manufac turing

process being observed. Some typical learning curves having different learning

rates are shown in Figure

1.

Learning curves follow the mathematical function

Y

=

KX

where

Y

K

X

= T h e cumulative unit number.

=T he number

of

direct labo r hours required t o produce the X t h unit

=T he number

of

direct labor hours required to produce the first

unit.

n

=

og The learning index.

log 2

@J

,

=The learning rate.

1

6 =T he progress ratio.

'Some au thors prefer to use cost as opposed t o direct labor hours. This author subscribes to the

school

of

thought th at believes direct labor hou rs are a m ore useful measure. T he primary reason is

that hourly compensation usually changes over time. Also, there is the additional problem

of

infla-

tion. In any event, direct labor hours can be easily converted into cost.

302


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T HE L E A RNING C UR V E

303

FIGURE

1

Typical Learning Curves

All

Requiring One Direct L abor Hou r

to Manufacture the First Unit (i.e., K = 1)

1.0 J-

1

10

100

1000

A

basic introduction to learning curves is provided by Carlson [28]. Various

authors have sometimes referred to the learning curve and related concepts by

other names such as the progress curve, the improvement curve, and the ex-

perience curve. In this survey, the term learning curve will be used throughout,

Th e learning curve began receiving attention du ring World W ar

11

as govern-

ment co ntr ac tor s searched for ways which they could use to predict costs an d time

requirements for construction

of

ships and aircraft to be used

to

conduct the war.

Crud e at tempts to use the data generated by government shipbuilding contrac tors

during the early phases of the war were published by Montgomery

[69] i n 1943

and Searle [79] in

1945.

It wasnt until after the war that aircraft production data were utilized by

Alchian [3] [4] in an at tempt t o compress the aircraft production experience of

World W ar I 1 into a study relating th e aforementioned experiences to the W right

phenomenon. In

1956,

Asher [8] put most of the military World War

11

and

im-

mediate post-World War 11 experience into focus by publishing his classic stud y.

This stu dy is particularly impo rtant because it summarizes much of the un-

published literature of that era.

Th e experiences

of

manufacturers with the learning curve phenomenon led

to its gradual adoption by private enterprise after the war.

I t

is with that

ex-

perience tha t this survey is concerned. Readers wh o ar e interested in the learning

curve experience of the war years are referred

to

Asher

[8].


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LEARNING CURVE GEOMETRY

Many geometric versions

of

the learning curve have been p roposed since the

initial discovery by Wright. The more well-known models are:

1 . Th e log-linear model.

2. Th e plateau m odel.

3. The Stanford-B model.

4. The DeJong model.

5 .

Th e various models ar e well described by Carlson (281

[29],

and interested readers

are referred to these two articles. T he various m odels are depicted in Figure 2.

Th e S-model (i.e., cubic L-C).

FIGURE

2

Various Learning Curve Models All Having the Same Value

of

Y

at

I00 Units

s

The reason for the search for something other than Wrights log-linear

model stems from the fact th at th e linear model does not always provide the best

fit in all situations. Garg and Milliman [41] describe the case w here the Boeing

Company found th at the Stanford-B model was the best fo r the manufacturing of

the Boeing

707

from the standpoint of describing ac tua l experience. A modified

version of the S tanford -B model was used t o inco rporate design changes

on

the

Boeing

707.

The essential point is tha t although the log-linear model has been, an d still

is,

by far the most widely used m odel, so m e manufacturers have fou nd oth er models

that better describe their experiences. Th rou gho ut the remainder of this paper we

will be assuming the log-linear model unless explicitly st ate d otherwise.


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THE LEARNING CURVE

305

PARAM ETER ESTIMATION

Par am eter estimation is particularly imp orta nt because it allows manufac-

turers to more carefully plan their activities. The earliest study conducted in a

search f or factors affecting the parameters of the learning curve was by Alchian

[3] [4]

on wartime air fram e data . Alchian fou nd that fitt ing learning curves to the

aggregate past performance of a single manufacturing facility in order to predict

the future could result in a significant margin of error. This study was particu-

larly significant because airfram e manufacturers had , by far a nd in large, been

operating on the assumption of an 80 percent learning curve. A nd , this assump-

tion did not ta ke into consideration the m argin of erro r no r differences between

airframe types.

Hirsch

[50],

in a comprehensive stud y

of

seven different machines built by a

single manufacturer, concentrated on the slopes of th e learning curves. H e fou nd

that the individual progress ratios ranged from 16.5 t o 20.8 percent. In a subse-

quent study on eight products m ade by the same ma nuf actu rer, Hirsch

[51]

found

that the progress ratios varied between 16.5 and 24.8 percent.

Cole [35], in his 1958 California survey of non-aircraft companies, con-

cluded that there was very little difference in progress ratios between different

types of manufacturing studies (18 t o 23 percent). Cole also concluded that there

was no cau sal relationship between th e slope and th e first unit cost for different

products. Coles conclusion tha t a K

-

relationship did not exist was in disagree-

ment with Asher

[8].

A nd , to this writers kn owledge, this inconsistency has never

been resolved.

In th e period 1966-1967, three sep ara te studies were published whose central

focus was on the predictability of the learning curve parameters. Baloff [lo , in

his study of twenty-eight separate cases of new products an d new process star tup s

occurring in five separate companies in fou r different industries, f ou nd th at the n

parameter varied widely. Billon [19], in his study, searched fo r regularity in learn-

ing curves in order to improve forecasting. The study consisted of five distinct

manufacturing programs an d fifty-four produc ts with three separa te manufac-

turers. Billon concluded that the slope tends to vary am ong firms m anu factu ring

similar products, a mo ng nonsimilar products m anufactured by a single firm , and

also amo ng various models of a basic product type produced by a single firm.

Subsequently, in 1967 Baloff 111 described the results

of

a n empirical ap -

proach to estimating the learning curve parameters using manufacturing ex-

perience and experimental studies

in

group learning. The primary focus of the

paper was on estimating n, given a reliable me asure of

K.

In other words, the ap-

proach assumed a K - n relationship existed. The study was conducted on steel

and airframe industry data. The results were sufficiently interesting to suggest

further work but could not be considered conclusive.

The parameter prediction dilemma still exists today. Two studies published

by Yelle

[91] [92]

utilized the disaggregation-aggregation pproach described by

Conway an d Schultz [37]. Th e results of the first study showed som e promise, but

since a single product was studied th e conclusions tha t can be draw n f rom it are


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306 DECISION

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limited. Then, in

1976,

Yelle

[92]

developed a theoretical framework for cir-

cumventing the power fun ctio n add itio n problem described by Conway a nd

Schultz

[37].

Further work is needed in the general area

of

parameter prediction.

Academicians as well as practitioners seem t o have neglected this area for the last

ten years.

LEARN ING

At a macroscopic level the learning curve includes two categories of learning.

They are labor learning and organizational learning. Hirschmann

[52]

claims that

the t w o ways to improve learning lie in t he inherent susceptibility of the labor in

an o peration to im prove and the degree to which this susceptibility is exploited by

the organization.

Labor Learning vs. Machine Learning

Op era tion s that have a high degree of labor content

or

are,

in

other words,

paced by labor can be expected to have much steeper slopes than operations

that

are machine paced. Hirschmann [53] and Jordan

[59]

reviewed airframe

manufacturing data. Both auth ors estimated tha t the proportio n of machine-

paced labor had historically affected the slope of the learning curve in approx-

imately the following way:

Machine-Paced Labor Learning Progress

as a percent of total labor) Rate Ratio

25

To

80 20

Yo

50% 85

15

15 90Yo 10

The only definitive empirical study done on this topic was conducted by

Hirsch

[ 5 1 ] .

Hirsch found that machining progress ratios were much smaller than

assembly progress ratios. Assembly progress ra tios were approximately two times

as

large

(25.6

percent vs. 14.1 percent). Thus Hirschs study established that the

progress ratio decreases as the proportion of machine-paced labor to total labor

increases.

The Learning Curve and Labor Slandards

T he most widely used application

of

the learning curve has been as an aid in

setting labor standards. When new

or

unskilled operators per form a task f or the

first time, they cann ot be expected to d o

so

in what w ould be considered t o be a n

acceptable time span. A certain period of time

or

number

of

cycles must be

allowed for the operator to gain familiarity with the necessary movements in

order to build up speed. The relationship between the learning curve and the


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LEARNING

CURVE

307

stan dar d time is shown in Figure 3 . Some of the better articles which address the

relationships between the learning curve and the s tand ard time ar e by Corlett and

Morcombe

[38],

Hancock

[47],

Kilbridge

[62] [63],

and Thomopoulos and

Lehman [83].

FIGURE 3

Relationship Between the Learning Curve and the Standard Time Per Cycle

30 t

U n s k i l l e d o p e r a t o r

2 0

I

k i l l e d o D er at ar

W

d

10

I

S t a n d a r d

T i m e

0

1

200

I

300

UNITS

One of the difficulties associated with setting standards using the learning

curve is that , in many situations, op erato rs possess

a

certain degree

of

skill gained

on other jobs. This tends to make the standard-setting procedure quite difficult

because op era tor s who have achieved a degree

of

speed on o ther job s will require

fewer cycles to reach the standard time. This problem is addressed by DeJong

(391. DeJo ng developed formulas to ap proxim ate the fall in cycle time when mak -

ing time studies given that residual skill resulting fro m prior experience exists.


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308 DECISION SCIENCES

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The Problem of Incentives

Operators accustomed to earning good wages on an incentive system n atu-

rally resist being transferred to another job within the plant. The source of this

resistance is the possible d ro p in incentive pay du ring the learning period on th e

new job . Janzen [58] presents a qu antitative method fo r handling a n experienced

opera tors wage decrease when he is given a new jo b of th e sam e general type tha t

he had been performing on an incentive basis. A complexity index is calculated

and used in conjun ction with the learning curve to determ ine how much time

will

be allowed for the operator to attain standard time and the incentive he will be

paid during their period. Baloff a nd M cKersie

[I41

subsequently proposed th at a

reliable sliding norm with incentives tied to that norm is what is needed.

Turban [85] suggests handling the problem of incentive wage losses by set-

ting temporary time standards in accordance with the learning curve. Purdue

labor learning tables are introduced to construct the temporary standards on a

week-by-week basis. T he most im portant finding of this study was tha t an incen-

tive during the learning period leads t o ope rat or s learning faster, thus sh ortening

the learning period. In yet another study, Broadston [25] proposed that using

variable time sta nd ard s would m ore nearly meet the needs of a wage incentive

system.

The situation where a production team is used in manufacturing presents

problems in the standard-setting process. Occasionally, a member

of

the team

will have to be transferred or will leave the organ ization. This requires the infu-

sion of a new inexperienced worker in to the team. T h e regular mem bers of the

team will resent this because the new mem ber, du e to his inexperience, will reduce

the outp ut of the w hole team while he learns. B arron [IS] describes this problem

and suggests some methods for handling this type of situation during the new

members learning phase in order that the regular members

of

the team d o not

have to take a cut in pay while the new member is learning.

Interruptions in the Learning Curve (i.e ., Relearning)

Interruptions or discontinuities in the learning curve generally occur when

new model changes are introduc ed, the design of the product is chang ed, o r in the

case of intermittent production on the same product. T hese interruptions lead to

a learning loss on the p art of op erato rs who originally performed the task.

Hall [46] suggests tha t design chang es lead t o tw o costs:

1.

Th e cost of added design less the quoted cost of the design rem oved.

2. Loss of learning-resulting in not being ab le

to

produce a n assembly a t the

full quantity contracted.

Hall focused on a practical way of factoring in a new design change into the

learning curve after the first unit is produ ced. Simple graph ic techniques a re pro-

posed to determine the cost in hours of major design changes.


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CURVE

309

Anderlorh [6] focused on p rod uctio n breaks between man ufa cture r lots

and the resultant

loss

of learning which takes place. Five fa cto rs associated with

loss of learning are identified. Baloff [12], Co ch ran [34], Carlson and Rowe [30],

Ho ffm ann [55], and Towill [84] also address this problem.

Organizational Learning vs. Labor Learning

T he learning curve should be thought of as a n aggregate m odel in the sense

that it includes learning from all source s within th e firm. O n a m acroscopic b asis

one may view the learning curve as a model which represents labor learning as

well as m anagerial

or

organ izational learning. Hirsch [50] in his study fo un d that

approximately 87 percent of the changes in direct labor requirements were

associated with changes in technical knowledge (a form

of

organizational learn-

ing).

Wyer [90], using aircraft industry dat a, makes the point th at the extent of th e

cost decrease that can be anticipated is associated w ith:

1.

The complexity of the product.

2. Th e amou nt of planning done.

The second point is particularly important as it is primarily related

to

organiza-

tional learning. T he quality of managerial planning is reflected in the slope of the

learning curve. Go od p lanning results in a flatter learning curve du ring the early

learning phase d ue to lower initial unit costs.

Lun dberg [67] published a n article which is closely related t o W yers wo rk.

Lundbergs major point is that there is a direct relationship between the quantity

of articles to be produced an d the am oun t

of

eff or t management is willing to put

into the pre-production planning phase. Stated simply, the larger the lot, the

bigger the organizational effo rt and the flatter the learning cu rve during the in-

itial learning period.

Hirschmann

[52]

uses petroleum refining as an example of where the learn-

ing curve might be thou ght to be inapplicable. H e proves that the learning curve

applies in the petroleum refining industry and tha t this is du e to organizational

learning (i.e ., technological learning) and not labor learning. T he essential point

is that th e learning observed in this indus try cant be du e to direct labor learn ing

as direct labor is practically nonexistent in the pe troleum refining industry.

Th e adap tation function proposed by Levy [66] attem pts to put organiza-

tional learning in perspective. Levy believes tha t the plann ing process can b e im-

proved through a better understanding

of

how the individual worker as well as

the firm have historically adapted

to

past learning situations. Th e for ma l training

and equipment replacement areas are used to illustrate how decision m aking was

improved du e to a better understanding of past behavior.

Bodde

[20]

summarizes some of the important issues concerned with

organizational learning and labor learning. This article is recommended to

readers who are interested in the use of the learning curve in manufacturing

management.


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31C DECISION SCIENCES

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FORECASTING LABOR REQUIREMENTS

The learning curve literature has not formally addressed in any great detail

the idea of forecasting labor requirements using the learning curve. This probably

emanates,from the fact that m uch of the literature addresses the problem of set-

ting time standards utilizing the learning curve. Then, overall labor force re-

quirements are obtained indirectly by converting from time standards. With

respect to forecasting the required w ork force, two points deserve special atten-

tion. Th e first point is that for

a

fixed labor force, capacity expands automatical-

ly as learning takes place. There are significant implications in this from the ag-

gregate planning point

of

view. The classical literatu re on aggregate planning did

not consider the learning curve as one

of

its elements until Eberts work [40] was

published in 1976. Authors who touch upon this are Andress

[7],

ochran [34],

and Hartley [48].

Th e second point which deserves special mention is the one made by Russell

[78]. Russell elaborates on the ramifications

of

adding and subtracting parallel

production lines. The theory as proposed states that doubling the num ber of p ro-

duction lines will double the quantity produced. But, the cumulative average

number of units produced by each production line remains the same. The im-

plication here is

that

expanding a single production line in order to increase out-

put will accelerate the learning process. Therefore, in making a decision to ex-

pand, the advantages and disadvantages of having two parallel production lines

as opposed to

a

single larger production line should be weighed carefully. Both

Baloff [12] and C ochran [32] discuss this point in a tangential way.

PLATEAUING

The phenom enon of plateauing was first observed by Conway and Schultz

[37] and subsequently explored in detail by Baloff [lo] [13]. The two phases of

plateauing are depicted in Figure 4. T he first phase consists of the initial or start-

up phase. This is the early manufacturing history of a product. The second phase

represents the steady-state phase of the learning curve or, in other words, the

point a t which learning ceases.

Machine-Intensive Manufacturing

Baloff [101 studied plateauing in machine-intensive manufacturing. The

study consisted of twenty-eight separate cases of new product and new process

startups that occurred in five separate companies in four different industries.

Heavy emphasis was on the steel industry. P lateauing was observed in twenty out

of twenty-eight cases.

Labor-Intensive Manufacturing

Baloff [131 explored the plateauing phenomenon in labor-intens ive manufac-

turing. Three labor-intensive industries were studied; auto assembly, apparel


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FIGURE 4

The Two Phases of Plateauing in

the

Learning Curve

31 1

manufacturing, and the production of large musical instruments. In the musical

instruments industry, only one-sixth of the products studied had a steady-state

phase.

N o evidence of plateauing was observed in apparel m anu factu ring for the

three cases examined. Auto assembly had plateauing in 75 percent

of

the situa-

tions studied.

Th e general conclusion which can be drawn fro m the two studies by B aloff is

that plateauing is much mo re likely to occur in machine-intensive industries th an

it is in labor-intensive industries. O ne possible ex planation for this is tha t p lateau-

ing could be strongly associated with labor ceasing to learn. And, in machine-

intensive manufacturing, this is likely to happen much sooner because the pro-

portion o f machine-paced labor (to total labor)

is

mu ch higher while the progress

ratios are smaller. Also, in machine-intensive manufacturing, the steady state

phase could be associated with managements unwillingness to invest more

capital in order to beget the technological improvem ents necessary fo r the learn-

ing process to continue. Hirschmann [52] offers still an oth er possible explana tion

for plateauing. Hirschmann makes the point that skepticism on the part of

management that improvement can continue may in itself be a barrier to its con-

tinuance. This skepticism may lie in the fact that new goals are not set once

previously defined goals have been achieved. And, lacking new goals, managers

do not have incentives to motivate themselves. This position is somewhat sup-

ported by Conway and Schultz

[37]

who found that two products that had

plateaued in one firm continued down the learning curve when transferred to

other firms. Tw o other articles related

to

plateauing t o which readers a re referred

are Goel and Becknell [42] and Knecht

[a].


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TECHNICAL KNOWLEDGE AN D INVESTMENT

Technical knowledge a nd investment are insep arable in the sense that invest-

ment begets technical knowledge which in tu rn results in lower costs as learning

takes place. Hirsch [50], in his study of machine building, demonstrated the im-

portance of the effect of changes in technical knowledge. H e fou nd that ap prox-

imately 87 percent of the changes in direct labor hour requirements were

associated with changes in technical knowledge.

Hollander [56] [57], in his pioneering study of D uP on t rayon p lants, fou nd

that

10

t o 15 percent of the increased efficiency

of

the plants was du e to the effect

of plant expansion. The remaining 85 to 90 percent was accounted for by

technical change. The author concluded that over

85

percent of the unit cost

reductions (due to technical change) at each plant depended u po n techniques that

required investment. Unit cost reductions that required replacement investment

were of special importance. Hollanders recommendation was that less weight

should be given to investment in plant and equipment similar to that already in

existence and more weight placed on the insertion of novel technology into

manufacturing.

1 .

2.

Th e main co nclusion drawn by Sheshinski is that efficiency gro wth is correlated

with the level

of

investment and that the large residual which is left can be ex-

plained by technological learning.

In [53] Hirschmann suggested that the relationships of learning curves to

depreciation an d capital investment indicate that depreciation ha s been more th an

adequate to provide replacement capital. In other words, technological progress

decreased costs mo re tha n inflation increased them.

Sheshinski [SO] postulated that:

Cumulative experience depends on cumulative gross investment.

Cum ulated experience depends on cumu lated ou tpu t.

MANAGEMENT CONTROL

A management control system may be thought of as that system of inter-

woven checks an d balances tha t mo nitors the activity of a firm. The fundam ental

purpose of a management c ontro l system is to help man agement assess perfor-

mance at various levels and indicate where remedial action is needed. In other

words, the managem ent c on tro l system is the primary mechanism used t o assess

managerial effectiveness. And, the learning curve is related to the management

control process because it is used by management for planning and goal-setting

purposes.

Young

[93]

states that there are five problems that complicate the isolation

of the reasons fo r the learning curve slope decline. T hey are:

I . Overestimation of initial costs in orde r to protect oneself.

2.

Shifting workers from direct to indirect status and vice-versa.

3.

Changes in manufacturing methods an d tooling.

4. The manufacturing lot size and material availability.

5 .

Con tinual engineering changes.


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313

The Learning Curve and B udgeting

Summers and Welsch in

[82]

make the point that the sta nda rd cost concept

implies no learning (i.e., that the learning curve is horizontal). Therefore,

if

learning is taking place over time, budget st an da rds based upon the sta nd ard cost

concept are apt to be excessively liberal or tight depending on where various

op erato rs are positioned on the learning curve. Th e resultant variance reports ar e

likely to be misleading. They conclude that inclusion of the learning curve in

budgeting should improve managerial planning and control of operating costs.

As implied in Figure 3 , this requires a knowledge of the operators previous ex-

perience as well as his current position on the learning curve with respect to the

standard. Th e autho rs suggest that it is also possible t o inco rpo rate a learning

effect variance to measure performance. Bump

[27]

also suggests tha t the learn-

ing phenomenon

will

wreak havoc with variance reports and that the inclusion

of

the learning phenomenon

in

setting the stand ard cost would lead t o mo re mean-

ingful reports for manag ement co ntrol. O rdinarily s tan da rds are set once a year.

A significant am oun t of learning can tak e place during o ne year.

I f

a firm uses the

approach of estimating the expected average standard cost over the year for

budgeting purposes, the learning phenom enon will accen tuate unfavorable

variances over the latter p art of the year. R eaders are referred to Harvey [49] for

additional reading in this area.

The Learning Curve and Breakeven Analysis

Brenneck [23) examines the effect of the learning curve on variable cost per

unit .

As shown in Figure 3 , the cycle time per unit will decrease as long as learn ing

takes place.

As

the cycle time decreases, both the per unit direct labor cost and

variable cost

will

drop. The conclusion that Brenneck draws is that learning

curves should be used in conjun ction with traditional breakeven analysis in ord er

to better appro xima te the variable cost per unit. This is because th e variable cost

per unit will change with volum e produced as long as learning exists, an d trad i-

tional breakeven analysis assumes that v ariable cost per unit is a co ns tan t. Mcl n-

tyre

[68]

and Pegels

[75]

provide additional insight on this topic.

Man power Scheduling

Whenever the learning curve phen om enon exists, it must be considered when

making out manpower schedules.

A

knowledge and understanding

of

the learning

curve makes it possible to project m ore accurate manpower requirements in ad -

vance. Au tho rs who add ress this issue are Brenneck

241,

Katz

[60],

Shroad

[81],

and Wertmann [87].

When o ne department depends upon ano ther for its inpu t, serious inventory

problems can occur

if

the departments are on d ifferent learning curves. Th e use

of learning curves to schedule manpower in the t w o departm ents in such a

w a y

that imbalances d o not occur is discussed by C oc hr an

[33] [34].


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Behavioral Implications of the Learning Cw ve

One

of

the fundamental ingredients

of

any manag ement con trol system is the

behavioral effect it has o n key employees. W hite [88] suggests it is desirable f or

managem ent t o predict expected improvem ent in advance . Goal-setting is a

proven ingredient

for

success in business. Yet Hirschmann

1521

warns against

wha t he calls a ceiling psychology. The ceiling in this case is set using the learn-

ing curve and then management works towards achieving the target. As

Hirschm ann sees it, once the goal is reached, in many instances mana gem ent do es

not forge ahead t o drive its costs down further. This is undoubtedly d ue to th e

fact that m anagements incentive is the target th at it set for itself. A nd , once th at

goal is attained, the motivation t o improve disappears. In othe r words, th e target

set with the use

of

the learning curve becom es a self-fulfilling prophesy .

COST REDUCTION PROGRAMS

Cost reduction programs a re very impo rtant for obvious reasons. Two of the

more fruitful areas for cost reduction program s are the pre-production planning

and the product-redesign areas.

FIGURE

5

The Effect of Organizational Planning Effort

on the Initial Phase of the Learning Curve

1

m

6

oor planning

100

10

1

1 10 100 1000

CuPpILbTIVX

m R OF

UUITS


14/27

19791

THE LEARNING CURV E

315

Pre-Production Planning

Th e effect of significant organizational planning in the pre-production stage

is

to

flatten out the initial phase

of

the learning curve. Stated another way, the

more planning a firm does p rior to manufacturing a prod uct, th e lower the value

of the K parameter in the learning curve model. Becker and Baloff [I61 and

Bhada

[I71

make this point. Th e ramifications

of

organizational planning become

quite obvious w hen o ne views Figure 5 . Even thou gh the p rod uct cost will

follow

the learning curve, effective planning in the early stages will significantly reduce

the initial cost. T he area between the tw o functions may be thou ght of as repre-

senting the potential cost reduction du e to planning. If it is mo re costly to plan

properly, then the potential cost reduction m ust be decreased by this additio nal

cost.

Supply-demand imbalances during the production phase are addressed by

Abernathy and Baloff [ I ] The authors suggest that careful planning at the

production-marketing interface would help prevent costly imbalances du e to the

rate

of

increase in productivity being different fro m th e rate

of

increase in sales.

Redesigning

Pr ior t o redesigning a produc t fo r lower cost, it will be necessary to estim ate

the engineering effort required t o d o the job . Both the product technology an d

the organ izations engineering skills will have to be appraised. Bruns

[26]

suggests

that the learning curve can help. In his article he presents a unique two-

dimensional model relating the engineering learning curve to the production

learning curve. Th e focus of the mo del is on helping man agement estimate how

many engineering design passes are needed to drive the product cost down to

some predetermined target, T he model is unique an d is highly recommended for

readers interested in redesigning products to reduce costs.

PURCHASING DECISIONS

Purchasing and bidding decisions are made daily by business firms. The

learning curve can be a valuable aid in the decision-making process. T he potential

contribution of the learning curve lies

in

the fact tha t a firm can evaluate learning

on its own products (bidding) as well a s on products

of

its suppliers (purchasing).

Bidding

When bidding o n a n order, it is impo rtant to know what the costs are now as

well as what they will be in the fu ture. The value

of

the role of the learning curve

in the bidding process lies in the fact that it allows

a

firm t o project its costs out

over an entire order and quote or bid accordingly. If the quote is for delivery

sometime in the future, then the curren t costs of the firm may not be relevant at

all for bidding purposes. If the qu ot e is for imm ediate delivery, then the learning


15/27

316 DECISIONSCIENCES [Vol. 10

which takes place during the time required to m anu factu re the lot is all that is

relevant. Readers are referred to Boren [21] for more information in this area.

Evaluation

of

Supplier Q uotes

Th e learning curve can be helpful in evaluating quo tes fro m suppliers. Most

quotes include quantity discounts for purchasing larger volumes of materials.

Rice [77] proposes evaluating a vendors quotes using the learning curve. The

method suggested requires that the per-item price be plotted against volume on

log-log paper. Rice concludes tha t this process should yield a straight line. If th e

process does not yield a straight line, then the vendor is probably n ot qu otin g ac-

cording to learning in all cases. Those quotes which appear to be out of line

(peaks) should be renegotiated with the supplier prior to making a decision on

how much to buy. Readers are referred to

[ 5 ]

and

(75)

for o ther reading in this

area.

The Learning Curve and Economic Order Quantity

Th e only work of any significance done in this are a is by Keachie an d Fo n-

tana [61]. The article deals with the learning curve effect on the calculation of

economic order quantities using the classical formula. The study assumed inter-

mittent production with large enough lots

so

that the learning phenomenon

would occur within a given lot. It was demonstrated that the traditional lot-size

formula yielded answers that were smaller than optim um . Th e underlying reason

for this is that the traditional formula assumes a constant manufacturing unit

cost.

NON-MANUFACTURING APPLICATIONS OF THE LEARNING CURVE

Until recently, the learning curve was primarily thought synonymous with

manufacturing activity of som e sort and /or cost control. In the last few years,

however, the learning curve has made in roa ds into other areas. Those areas are

discussed below.

The Learning Curve

and

Accident Experience

Greenberg [43] 441 applied th e learning curve concept to the industrial acci-

dent experience in the petroleum industry. The study encompassed forty-seven

firms and a total of 163 departments.

The focus of the study was on

USA

standard 216.1. On e of th e statistics

defined by this s tan da rd is listed below:

No.

of Disabling Injuries x l,OOO,OOO

No.

of

Manho urs Worked

Disabling injury frequency rate =


16/27

19791

THE LEARNING

CURVE

317

Greenberg found that this method of reporting accidents was very misleading.

The fundam ental reason for this is that the denominator is in units

of

time rather

than units of production. Thus, learning is not taken into consideration over

time. The crux

of

the matter is that 216.1 does not include a productivity

measure. By using hour s (time units), an d given th at productivity per ho ur has in-

creased over time, accidents per unit decrease over time.

Greenberg found that the incidence of accidents was fou nd t o be highly cor-

related negatively with productivity. In oth er words, accidents per unit produ ced

decreased as management gained productive experience. When accident ex-

perience is computed on a per-item basis and is plotted against cumulative pro-

duction, a learning curve accident model emerged of the form Y =KX".

In yet another study, Greenberg [45], using mining industry data,

demonstrated that mining accidents also conformed to the learning curve model.

On e important observation which should be made ab out Greenberg's studies is

that he used publicly available data. For years, the nonavailability of data has

been the bane of the existence of researchers interested in the learning curve

phenomenon.

The Learning Curve

and

Warranty Maintenance

Kneip [65] selected two products an d proceeded to accum ulate field service

dat a on the two products. Th e objective was to ascertain if the learning curve

could adequately describe the relationship

of

a

product's maintenance

re-

quirements during the warranty period to cumulative production experience. Th e

situation is depicted in Figure 6. The results of regression analyses on the

two

products proved th at there was a strong relationship between the am ou nt of ser-

vice required to perform warranty maintenance and cumulative production ex-

perience because the quality of the product improved as more units were

manufactured. The relationship was of the classical form Y = KX", and the results

were significant at the

.001

level.

In a different kind of study, Clark

[31]

used learning curves t o predict th e re-

quired size

of

a plant's maintenance force. The assumption was made that

maintenance workers learn and that this learning is adequately described by the

classical model Y = KX". Clark was able to successfully demonstrate that the

learning curve was useful in predicting the size of a maintenance force over time.

The Learning Curve, Cost Allocation, and Income Reporting

The accounting profession has for years followed the practice of reporting

actual costs in the period in which those costs are incurred. From t he product-life-

cycle point of view, this practice leaves something to be desired. It inevitably

results in heavy losses during the initial phases

of

the product life cycle due t o re-

quired initial investments an d the usual high cost o n the*firstunits manufactured.

In th e latter stages of the product's life cycle the opposite occurs. The firm reaps

the benefits of low per-unit costs due to learning and also the benefits derived


17/27

318

DECISION SCIENCES

FIGURE

6

The Relationship of a Product's n ic e Requirements

During

Its

Warranty Period

100.

10 4

1

100

10

1

.

1

10

100

CUMRATIW F'RODUCTION

8 S O N I C 0 C d h

[Vol. 10

1 10

100

m T I V E PWDUCTIOU

b.

Somice

burr


18/27

19791

THE LEARNING CUR VE

319

from having made investments in the early phases. Morse

[70]

states that the

practice of reporting costs in the period incurred is inconsistent w ith the accoun t-

ing professions definitions of the concepts of matching an d materiality.

Morse takes the position that the allocation of costs over the entire produ ction

life cycle of the product with the help of the learning curve would m or e closely

meet the matching and materiality criteria.

T he procedure suggested by M orse is to use the learning curve to arr ive at an

average unit cost over the entire prod uct life cycle. The n costs ar e charged o n a

per-period basis using the average unit cost projected by the learning curve. The

net effect is that income is raised in the early phases and lowered in the later

phases of the entire production life cycle. I n oth er words, a n income smoQthing

effect takes place. Morse concludes that this approach more closely meets the

criteria suggested by Bierman and Davidson

[18].

Readers are referred to M orse

[70] (711

for further reading o n this topic.

Recently, Harvey [49] built up on the works of Bump [27] and Summers and

Welsch

[82].

He developed m odifications to the learning curve in ord er t o better

observe the financial effects of erro rs in parameter estimates. T he financial area s

studied were cash flow, profitability, and the internal rate of return.

MANAGEM ENT STRATEGY

The term management strategy is used here synonymously with policy mak-

ing at the to p management level. Th rou gho ut this paper, topics

of

a

policy nature

have been discussed without explicitly so stating. In this section, however, the

view is policy mak ing at the to p level. The policy-making ar ea is particularl-y im-

por tant because it has been difficult to find suitable cons truc ts with which t o

describe this organizational activity adequately. As far as the learning curve is

concerned, Abernathy and Wayne

[2]

and Conley

[36]

have done most of the

work in this area.

Conley

[36]

describes the use of a modified version

of

the learning curve

called the experience curve. T he experience curve is utilized t o m ak e m ajo r deci-

sions in the marketing area which ultimately affect ma nuf actu ring ope ratio ns

significantly. The major assumption made is that the m anufac turer who ha s pro-

duced the most units probably has the lowest unit cost du e t o learning. T he im-

plication from a strategy viewpoint is that successful firms ar e those th at follow

the strategy of achieving market do mi nan ce by comm itting themselves to becom-

ing the largest manufacturer of a product. As ma nuf actu ring experience is

gained, th e lowest unit cost is achieved via the learning curve phenomenon. Th en ,

market do minance becomes a reality by using price a s a competitive weapon.

The experience curve ideas as put forth by Conley were tested in another

study by Nathanson [73]. Nathansons work focused upon the use of price

Patrick Conley was a vice president of the Boston Consulting Group in 1970. His article [36] eflects

many of the ideas found in this group s publication [22]. Because

[22]

is not readily available, in-

terested readers are referred

to

[36].


19/27

320

DECISION SCIENCES [Vol.

10

forecasting a s a competitive weapon in the petrochemical industry; he coupled

statistical price forecasting with technological forecasting. This article is strongly

recommended as further reading since it is the only article known to this writer

that expands upon and validates the ideas expounded upon by Conley.

Abernathy and W ayne

[2]

used the Ford M oto r Co mp any s experience with

the Model T an d M odel A

as

an example of how the experience curve can be used

to explain policy-making behavior. Th e essential point mad e in this article is tha t

Ford pursued the learning phenomenon with a passion and succeeded in pricing

competition out of the market. The authors point out that this strategy leads to

organizational inflexibility and that this led to General Motors becoming the

leader in the long run. The tastes of consumers for automobiles changed, and

Fords policy was such that the organization could not react quickly to this

change as they were comm itted

to

a single policy of mass-producing a low-p riced,

no-frills automobile.

Readers ar e urged to relate the F ord experience (essentially on e model)

to

the

point made by Conley

[36].

Conley strongly recommends that a balanced port-

folio

of

products greatly reduces the risks of following a mass-production policy.

Th e essential point is that if F ord had h ad three or fo ur models to sell instead of

just the Model T , then they might have lost ou t on th e Model

T

but would have

had other m odels to su ppo rt the companys viability.

SUMMARY

OF

RECENT TREND S IN

LEARNING CURVE APPLICATIONS

Th e period

1935-1969

saw the learning curve literature describing applica-

tions within a restricted area. Almost all of the literature of this period focused

upon military applications followed by industrial applications of a cost-control

nature. The industrial applications focused upon the following topics:

1.

2.

Parameter estimation.

3.

4.

Classical cost control.

5 .

Purchasing and bidding functions.

One significant departure from this scenario was Hollanders study

of

DuPont

rayon plants

[56]

conducted in

1963.

Hollander addressed the relationship be-

tween technical change, capital investment, and increased productivity due to

learning. This significant study has not generated the attention it deserves, as

evidenced by the lack of subsequently published studies by othe r autho rs.

Then Greenberg

[43]

in

1969

applied the learning curve concept

to

occupa-

tional accident reporting in the petroleum industry. This is the first study of

which this writer is aware that applied the learning curve concept outside the

manufacturing environment and that also utilized publicly available data.

Various shapes of the learning curves.

Industrial engineering applications such a s setting time s tan dard s and incen-

tives.


20/27

19791

THE LEARNING CUR VE

32 1

Subsequent studies using the learning curve construct as an aid in better

understanding items of a public policy n atur e such as Greenbergs have yet to be

published.

In 1970,

the Boston Consulting Gro up

[22]

and Conley

[36]

proposed using

a

version of the learning curve (experience curve) to assess competitions ma nufac-

turing costs. This data in turn would be compared with internal data and then

decisions of a marketing strategy nature would result. The whole point of this

work was to make marketing and m anufacturing policy fo r the firm based up on

informational forecasts generated with the learning curve.

Morse [70] in 1971 was the next individual to do work of a non-classical

learning curve nature. Althoug h Morses work is in the accou nting a rea , i ts, foc us

is really on accounting philosophy and how some of those concepts can be better

achieved by the use

of

the learning curve

to

benefit society. Readers will recall

tha t Morse propo sed a cost allocation philosophy which would ultimately affect a

firms earnings per share significantly. This in turn would affect the perceptions

of the investing public as

to

just what the firms stock was really worth.

Then Abernathy and Wayne [2], in 1974, described the top management

policies of the Ford Motor Company (i.e., Model A and Model T) using the

learning curve model. T his article is the best published w ork o f which this au th or

is aware that sets the top management policies of a large corporat ion into

perspective using th e learning curve as a struc tural aid for explanatory purposes.

Readers ar e also urged to read Utterback and Abernathy [86].

Clearly, the learning curve construct has been fou nd useful in new areas du r-

ing the past ten years. T he general direction of these new applications focuses to a

great degree on the policy-making level of the business firm and on public- or

service-related issues. This is in s ha rp contrast to the classical indu strial engineer-

ing types of applications that were the focus of attention during the previous

three decades. In the following section of this pap er , areas fo r fu tu re research will

be suggested. Much needs to be d on e, particularly at the macroscop ic level as op -

posed t o the microscopic level of the period 1935-1965.

FURTHER RESEARCH

Th e potential areas for future research are indeed a bu nd an t in the learning

curve are a. B oth the so-called classical areas of learning curv e application as well

as the newer areas delineated in the previous section need mu ch mo re atten tion

from academicians as well as practitioners.

Parameter Estimation

Many issues in this general area still require further clarification. The

aggregation-disaggregation conc ept app ro ac h of estimating learning curves needs

to

be validated.

Identification of facto rs favoring an accelerated rate of learning is anoth er

promising area for futu re research. Within this area focus should be broug ht to


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322

DECISION SCIENCES

[Vol.

10

bear upon the relationship between organizational effort in the planning stage

and its effect o n th e initial K parameter as well as the slope of th e learning curve.

Also, it would be useful t o know when a process has gone fro m the sta rtu p to

a steady-state phase. T he relationship between the two phases, the cycle time, a nd

the production run time needs t o be clarified. Manag erial interest in the product

needs to be assessed from the standpoint of its effect on plateauing. In other

words, does a lack of interest on the part of managem ent create plateauing?

The research areas cited above should be directed as much as is possible to

estimating learning curves in advance of producing the first unit. Management

needs to know prior to making significant commitments of capital and talent

whether or not these commitments are going to be worthwhile. In additi on, the

areas

of

product costing, delivery commitments, scheduling, and raw materials

acquisitions would all benefit from more accurate learning curve estimates.

The Learning Curve and Aggregate Planning

With the sole exception of Eberts recent work [MI he aggregate planning

models that proliferate the literature

do

not include the learning curve as a com-

ponent. Given a steady work force, a s learning takes place out pu t increases du e to

increases in productivity per worker. An aggregate planning model that incor-

porates the learning phenomenon would yield more realistic information for

managerial planning purposes. The significance of new aggregate planning

models becomes increasingly ap pare nt when on e starts t o consider the effect of

better information on areas such as inventory policy.

Learning

Labor learning has received the most att enti on in th e literature for obvious

reasons. There are elaborate techniques designed to set labor standards.

Organizational learning and one

of

its major subsets, technological learning,

have frequently been mentioned in the literature. Yet, studies to factor out

these various types of le,arning from a single learning curve have not been pur-

sued. A better understanding of the contributions of each kind of learning is

needed. As o ne example for further study in this area, consider th at it has already

been established that different departments within the same firm have different

learning curves. How much of this is due to different organizational ar-

rangements between departments?

Within this area falls the phenomenon of workers and an organization

forgetting, to a degree, how t o manufacture a p roduct due to produ ction inter-

ruptions. Th e phenomenon

of

relearning needs more atten tion in the context of

the various components of learning. A re the relearning phenom enon a nd the idea

of organizational adaptation mentioned in [9] elated?

Financial Areas and the Learning Curve

In [52] the question is raised a s t o whether or not it is best to m odernize ex-

isting facilities or build new ones. Additionally, the comment is made that the


22/27

19791

THE

LEARNING CU RVE 323

relationship of the learning curve to depreciation and capital investment suggests

that depreciation has been more than adequate to provide replacement capital.

The role

of

the learning curve as

a

managerial decision-making aid in these tw o

areas needs t6 be explored and clarified.

Morse

[70]

proposed a cost allocation learning curve model. T he model, if

implemented, would have the tendency to change the reported earnings of a firm.

A fruitful area for future research would be to establish to w hat degree allocating

cost on his basis would change the value investors place on

a

firm.

The area of human resource accounting as proposed in [72] falls into the

financial category. Studies could be done to examine the effects

of

reporting the

learning potential of human resources as an asset. The value of this learning

potential would be projected by the use

of

learning curves.

Another question that needs answering is to what degree can the learning

curve be useful in providing information that would prevent over-building of

plant capacity.

The Learn ing Curve and Marketing Strategy

Every product has a life cycle. One unanswered question is how is the learn-

ing

curve related to the product life cycle? For example, is the phenomenon of

plateauing in the learning curve related to the mature phase

of

the product life

cycle? If there is a relationship here, the implications for strategic planning are

enormous. The work

of

Utterback and Abernathy

[86]

is certainly

a

beginning

here.

The Boston Consulting Groups studies [22] deserve further attention.

Nathansons article

[73]

touches upon the use of various indices (deflators) used

by this group. Further validation of Nathansons w ork is needed.

The use of the learning curve as a technological forecasting construct was

cited by the 1967 Organization for E conomic Cooperation a nd Development as

the most neglected area. Since then, a new journal,

Technological Forecasting

and Social Chan ge,

has been born. This journ al has served

as a

useful vehicle for

the dissemination of embryonic knowledge in this area.

Non-Manufacturing Applications of the Learn ing Curve

Greenberg [43] moved the learning curve into the accident-reporting a rea of

the federal government. This work should be extended further in to the formation

of public policy on industrial accident reporting, particularly with respect to the

way accidents are reported. The end result would hopefully lead to better

accident-prevention policies. The impingement effects

of

policy changes on

workmens compensation plans, civil suits, private insurance, and legal fees are

all areas for further investigation.

1.

Tw o other areas mentioned by G reenberg for future research are:

Th e use of learning curves to set acciden t con trol limits (i.e., like quality con-

trol limits) within a firm.


23/27

324 DECISION SCIENCES [Vol.

10

2.

The possibility that the automotive accident experience can be described by

the learning curve.

Extension

of

the work reported by Kneip

[65]

on warranty maintenance ser-

vice seems in order. Kneip used th e learning curve

to

relate service calls to produc-

tion experience. T he implications of extending this work

so

that warranty policies

are changed based on manufacturing experience has not been investigated.

Also,

relating this work to an overall marketing policy has yet

to

be done.

The Management-Economics Interface

Th e quality

of

the interface between th e managemen t profession an d the ap -

plied economist could be improved. The professional economist can undoubtedly

help managers to better understand t he learning curve phenomen on. O n the other

han d, m anagers need to be receptive t o help from economists. T wo very good a r-

ticles written by Hirshleiffer [54] and Preston a nd Keachie (761 help to bridge the

ga p between how a n economist looks at a firms cost functions an d the learning

curve. Pegels [74] is also recommended.

The Learning Curve and Management Strategy

Conley [36] and Abernathy an d Wayne [2] have don e the pioneering work in

applying the learning curve to top management policy making. Conleys ap-

proach focuses on marketing policy whereas Abernathy and Wayne focus

primarily on manufacturing policy. In effect, readers have only these two studies

available to themselves in this crucial top management area. The surface has

hardly been scratched. And, in this writers view, this area represents one of the

more promising areas fo r fu ture research for th e learning curve.

REFERENCES

Abernathy, W. J., and. Baloff. A Methodology for Planning New Product Start-ups.

Decision Sciences. Vol. 4,No. 1 (1973). pp.

1-20.

Abernathy, W. J., and K.Wayne. Limits of the Learning Curve.

Harvard Business Revie w.

Alchian. A. Reliability of Progress Curves in Airframe Production. Santa Monica, Calif.:

RAND Corporation, April

1950.

Report

260-1

Alchian. A. Reliability

of

Progress Curves in Air-Frame Production. Economefricu, Vol.

3

NO. 4 (1963).pp. 679-693.

Alden, R.

J

Learning Curves: An Example. Industrial Engineering, Vol. 6 , No. 12

(1974),

pp. 34-37.

Anderlohr,

G.

Determining the Cost of Production Breaks. Manugemenf Review, Vol. 58 ,

No.

12

(1 9), pp.

16-19.

Andress, Frank J. The Learning Curve as a Production Tool. Harvard Business Revie w, Vol.

Asher,

H.

Cost-Quantity Relationships in the Airframe Industry. Santa Monica, Calif.:

RAND Corporation, July 1956. Report 291.)

Baloff, N. Manufacturing Startup: A Model. Palo Alto, Calif.: Stanford University,1%3.

Doctoral dissertation.)

Vol.

52,NO. 5 (1974).pp. 109-119.

32,NO. I(1954). pp. 87-97.


24/27

19791

THE LEARNING CUR VE

325

[lo ] Baloff, Nicholas. Startups in Machine-lntensive Produc tion Systems. Journal of Industrial

Engineering, Vol. 17, No. 1 (1966), pp. 25-32.

[1 I ]

Baloff, Nicholas. Estimating the Param eters of the Sta rtu p Model-An Empirical Ap-

proach.

Journal

of

Industrial Engineering,

Vol.

18,

No.

4 (1%7), pp. 248-253.

[121 Baloff, N. Sta rtup Manag emen t. IEEE Transactions on Engineering M anagemen t. Vol. EM-

[13) Baloff, Nicholas. Extension of the Learn ing Curve-Some Empir ical Results.

Operations

Research Quarterly,

Vol. 22, No. 4 (1971), pp. 329-340.

[I41 Baloff, N., and R. McKersie. Mo tivating Startu ps.

Journal of Business

(Chicago), Vol. 39,

No. 4 (1966), pp. 473-484.

[ I S ]

Barron , L. A. Learner Curves Boost Teams Outpu t. American Machinist. Vol. 102, No. 25

(1958), pp. 100-101.

(16) Becker, S., and N. Baloff. Organization Structure and Complex Problem Solving.

A d -

ministrative Science Q uarterly, Vol. 14, No. 2 (1%9), pp. 260-271.

[I71 Bhada, Y.K. Dynamic Cost Analysis.

Management Accounting, Vol.

52,

No.

1 (1970). pp.

[18] Bierman, H. r., and S.Davidson. Th e Income Concept-Value lncrement of Earnings Predic-

tor.

Accounting Review, Vol. 44,

No. 2,(1969), pp. 239-246.

[19] Billon, S. A. lndustrial Learning Curves and Forecasting Production Requirements.

Management International Review, Vol. 6, No. 6 (1966). pp. 65-96.

[20] Bodd e, David L. Ridin g the Experience Curve. Technology Review, Vol. 78,

No.

(1976),

pp. 53-59.

[2l ] Boren, W. H. Some Applications of the Learning Curve to Government Contracts. N . A . A .

Bulletin,

Vol. 46, No. 2 (1964), pp. 21-22.

[22] Boston Consulting Group . Perspectives on Experience. Boston, Mass.: B oston Consu lting

Group, 1970.

[23] Brenneck, R. Breakeven Charts Reflecting Learning.

N.A.A. Bulletin,

Vol.

40,

No. 10

(1959), p. 34.

[24] Brenneck, R. Le arning Curve Techniques for More Profitable Contracts. N.A.A. Bulletin,

[25] Broadston,

J.

A. Learnin g Curve W age Incentives.

Management Accounting,

Vol. 49. No.

[26] Bruns, J . H. Forecasting the Cost of Redesign. Machine Design, Vol. 42, No. 6 (1970), pp.

[27) Bum p, E. A. Effects of Learning on Cost Projections.

Management Accounting,

Vol.

5 5

[28] Carlson, J. G. How Management Can Use the Improvement Phenomenon.

California

Management Review, Vol. 3, No. 2 (I ] ) , pp. 83-94.

[29] Carlson,

J. G.

Cubic Learning Curves: Precision Tool

for

Labor Estimating.

Manufacturing

Engineering and Managem ent.

Vol. 71. No. 5 (1973). pp. 22-25.

[30] Carlson, J. G. nd R. J. Rowe. How Much Does Forgetting Cost?


Vol. 8, No. 9 (1976), pp. 40-47.

[31] Clark,

S.

Applying Learning Curves

to

the Maintenance Force.

Plant Engineering.

Vol. 21,

[32] Coch ran, E. B. New Concepts of the Learning Curve. Journal of Industrial Engineering,

[33] Coch ran, E. B. Learning: New Dimension in Labor Standards.

Industrial Engineering, Vol.

I341 Co chra n, E. B. Dyn amics of Wor k Standa rds.

Manufacturing Engineering and Manage-

ment,

Vol.

70, No. 4 (1973), pp. 28-31.

[35) Cole, R. Increa sing Utilizatio n of the Cost Quantity Relationship in Manufac turing. Journal

of


Vol. 9. No. 3 (1958), pp. 173-177.

[36] Conley, P. Experience Curves as a Planning Tool.

IEEE Spectrum,

Vol. 7, No. 6 (1970). pp.

17, NO. 4 (1970), pp. 132-141.

11-14.

Vol. 40, NO. 11 (1959), pp . 59-69.

12 (1968). pp . 15-23.

113-1

I S .

NO. I1 (1974), pp. 19-24.

NO. 8 (1967), pp. 126-127.

Vol. 11,

NO.

4 (1960), pp. 317-327.

I

NO. I (1969), pp. 38-47.

63-68.


25/27

326

DECISION SCIENCES

[Vol. 10

[37] Conway, R., and A. Schultz. The Manufacturing Progress Function.

Journul

of

Industrial

Engineering,

Vol.

10, No. 1 (1959), pp. 39-53.

[38] Corlett, E. N., and

V.

J. Morcombe. Straightening Out the Learning Curve.

Personnel

Munagement,

Vol.

2,

No.

6 (1970).

pp.

14-19.

[39] DeJong, J. R. T he Effects of Increasing Skill on Cycle Time and Its Consequences for Time

Standards. Ergonomics,

Vol.

1, No. 1 (1957). pp. 51-60.

[40] Ebert. R. J. Aggregate Planning with Learning Curve Productivity. Munugement Science.

[41] Garg, A., and P. Milliman. The Aircraft Progress Curve Modified for Design Changes.

Journal of Industriul Engineering, Vol. 12,

No. 1 (1961). pp.

23-27.

[42]

Goel,

S. N., and R. H. Becknell. Learnin g Curves Th at Work.

Industrial Engineering, Vol.

(431 Greenberg, L. The Application of Accident-Experience Learning Curves to the Study of Oc-

cupatio nal Accidents in th e Ame rican Petroleum Ind ustry. New York: New York University,

1969. (Doctoral dissertation.)

[44]

Greenberg, L. Measurem ent of the W ork-Accident Experience in the American Petroleum In-

dustry.

American Society of W e t y Engineers,

Vol. 15, No. 2 (1970), pp. 11-13.

[45] Green berg, L. Why th e Mine Injury is ou t of FOCUS.

Mining Engineering,

Vol. 23, No. 3

[46]

Hall, L. H. Experience With Experience Curves for Aircraft Design Changes.

N. A. A .

Bulletin,

Vol.

39, No. 4 (1957), pp. 59-66.

[47] Hancock, W.

M.

Prediction of Learning Rates for Man ual Operations. Journul of Industriul

Engineering, Vol.

18, No.

1

(1%7), pp. 42-47.

[48] Hartley, K. The Learning Curve and Its Application t o the Aircraft Industry.

Journul

of

In-

dustrial Econo mics,

Vol.

13, No. 2 (l S), pp: 122-128.

[49] Harvey, D. W. Financial Planning Information for Production Start-ups. Accounting

Review,

Vol. 51,

No.

4 (1976).

pp.

838-845.

[SO] Hirsch , W. Z. Manufacturing Progress Functions. Review of Econom ics und Statistics, Vol.

[ S l ] Hirsch, W. . Firm Progress Ratios.

Econometricu,

Vol.

24,

No. 2 (1956). pp. 136-143.

[52] Hirschmann, W. B. Prof it from the Learning Curve. Hurvurd Business Review , Vol. 42, No.

[S3] Hirschmann,

W.

B. Learning Curve.

Chemical Engineering,

Vol. 71, No. 7

(1964),

pp.

[54] Hirshleiffer, J . Th e Firms Cost Functio n: A Successful Reco nstructio n? Journal of Business

(Chicago), Vol. 35, No. 3 (1%2), pp. 235-255.

[ SS ] Hoffmann, J. R. Effects

of

Prio r Experience on Learning Curve Parameters.

Journul

of

In-

dustrial Engineering, Vol. 19, No. 8 (1%8), pp. 412-413.

I561

Hollander,

S.

The Sources of Increased Efficiency: A Case-Study of Du Po nt Rayon M anufac-

turing Plants. Princeton, N.J.: Princeton University, 1963. (Docto ral dissertation.)

[57] Hollander, S. Th e S ources of Increased Efficiency:

A

Study of DuPo nt Rayon Plants. Cam-

bridge, Mass.: M.I.T. Press, 1%5.

[58] Janzen. J. L. The Manufacturing Progress Function Applied to a Wage Incentive Plan.

Journal

of


Vol.

17.

No.

4

(I ), pp.

197-ulo.

[59] Jordan, R.

B.

Learning How to Use the Learning Curve.

N.A.A. Bulletin,

Vol. 39, No. 5

[60] Katz, R. Understanding and Applying Learning Curves. Automation, Vol. 16, No. I I

[61] Keachie, E. C., and R. J . Fontana . Effects of Learning on Optima l Lo t Size. Management

Science,

Vol.

13,

No.

2

(1966).

pp.

102-108.

[62] Kilbridge, M. P redeterm ined Learnin g Curv es fo r Clerical Operations.

Journal

of

Industriul

Engineering, Vol.

10,

No. 3 (1959), pp. 203-209.

[63] Kilbridge, M. A Model for Industrial Learning Costs. Munugement Science,

Vol.

8, No. 4

Vol. 23, NO. 2 (1976), pp. 171-182.

4,

NO.

(1972), pp. 28-31.

(1971), pp. 51-53.

34, NO. (1952),

pp.

143-155.

I (1964), pp. 125-139.

95-100.

(1958), pp. 27-39.

(1969), pp. 50-53.

(1962), pp. 516-527.


26/27

19791

T H E L E A R NI N G C U R V E

327

[64]

Knecht, G. R. Costing Technological Gro wth and Generalized Learning Curves. Operations

Research Quarterly, Vol.

25, No. 3 (1974), pp. 487491.

[65] Kneip, J. G. T he Maintenance of Progress Function. Journalof Industrial Engineering, Vol.

16, No. 6 (1965), pp. 398-400.

[66] Levy, F. K. Adaptation in the Production Process. Management Science,

Vol.

11,

No.

6

167) Lundberg, R. H . Lea rning Curve Theory as Applied

to

Production Costs.

S.A.E. Journal,

[68] Mcln tyre, E. V. Cost-Volume-Profit Analysis Adjusted for Learning. Management Science,

(691 Mo ntgom ery, F. Increas ed Produ ctivity in the Constr ucti on of Liberty Vessels. Monthly

Labor Review, Vol.

57, No.

5

(1943), pp. 861-864.

[70] Morse, W. J. The Allocation

of

Production Costs With the Use

of

Learning Curves. East

Lansing: Michigan State University, 1971. (Doctoral dissertation.)

[71] Morse, W. J . Reporting Production C osts that Follow the Learning Curve Phenomenon . Ac-

counting Review,

Vol.

47, No. 4 (1972), pp. 761-773.

[72] Morse, W. J. Use

of

Learning Curves in Financial Accounting. CP A Journal,

Vol. 44

o. 1

[73] Nat han son , D. M. Forec asting Petroche mical Prices.

Chemical Engineering Progress,

Vol.

[74] Pegels, C. C. O n Startu p or Learning Curves: An Expanded View. AII E Transactions, Vol.

(751 Pegels, C. C. Start U p or Learning Curves-Some New Appr oache s. Decision Sciences, Vol.

[76] Preston, L. E., and E. C. Keachie. Cost Functions an d Progress Functions: An Integration.

American Economic Review, Vol. 54, No. 2 (1964), pp. 100-107.

[77] Rice, J. W. Throw Prices A Curve .

Purchasing,

Vol.

69, No. 1 (1970). pp. 474 9.

[78] Russell, J.

H.

Progress Function Models and Their Deviations.

Journal of Indusfrial

Engineering, Vol. 19, No. 2 (1968), pp. 5-10.

[79] Searle, A. D. Productivity of Labor and Industry. Monthly Labor Review, Vol. 61, No. 6

[SO] Sheshinski, E. Tests of the Learning by Doing Hypothesis.

Review of Economics and

Statistics, Vol. 49, No. 4 (1967), pp. 568-578.

[Sl] Shroad,

V .

J. Control of Labor Costs Through the Use of Learning Curves.

N . A . A .

Bulletin, Vol. 46, No. 2 (1964), pp. 15-20.

[82] Summers, E. L., and G. A. Welsch. Ho w Learning Curve Models Can Be Applied to Pro fit

Planning.

Management Services, Vol.

7, No. 2 (1970), pp. 45-50.

[83] Thom opou los, N. T., and M. Lehman. The Mixed Model Learning Curve .

AIIE Transac-

tions, Vol.

1.

No. 2 (1969), pp. 127-132.

(841 Towill, D. R. An Industrial Dynamics Model for St ar t- up Managem ent.

IEEE Trunsactions

on

Engineering Managem ent,

Vol. EM-20, No. 2 (1973). pp. 44-51.

[85] Tu rba n, E. Incentives During Learning-An Application of the Learning Curve Theory and a

Survey of Other Methods.

Journal of Industrial Engineering,

Vol. 19, No. 12 (1%8), pp.

600-607.

[86] Utterback, J. M., and W. J. Abernathy. A Dynamic Model of Process and Product lnnova-

tion.

Omega,

Vol. 3, No. 6 (1975), pp. 639-656.

[87] Wertm ann, L. Pu ttin g Learning Curves to Work.

Tool Engineer,

Vol. 43,

No.

3 (1959), pp.

[88] White, James. The Use

of

Learning Curv e Theory in Setting Management Goals.

Journal of


Vol.

12, No. 6 (1961), pp. 409-411.

[89] Wright, T. P. Fa ctors A ffecting the Cost of Airplanes. Journal of Aeronautical Sciences,

1901 Wyer, R . Learning C urve Helps Figure Profits, Control Co sts.

National Association o fC os t

Accountan ts Bulletin,

Vol.

35, No. 4 (1953), pp. 490-502.

(1965), pp. B136-BI54.

Vol.

64

O. 6 (1956), pp . 48-49.

Vol .

24, NO . 2 (1977), pp. 149-160.

(1974). pp. 51 - 55 .

68, NO. II 1972), pp. 89-96.

1, NO. 3 (1%9), pp. 216-222.

7,

NO.

4 (1976), pp. 705-713.

(1945), pp. 1132-1147.

99-102.

Vol. 3, NO. 4 (1936), pp. 122-128.


27/27

328 DECISION SCIENCES [Vol. 1

[91]

Yelle, L. E. Technological Forecasting: A Learning Curve Approach. Indusfrial Manage-

ment,

Vol.

16, No. 1

(1974), pp.

6 - 1 1 .

[92] Yelle, L.

E.

Estimating Learning Curves for Potential Products.

Indusfrial Markefing

Managemenf,

Vol.

5

No.

213

(1 376),

pp. 147-154.

[93] Young,

S.

Misapplications

of

the Learning Curve Concept.

Journal

of

Indu strid Engineer-

ing, Vol. 17, No.

8

(1966). pp. 410-415.

the learninig curve historical review yelle

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