Printer Friendly

The learning curve and production standards : learning implications.

The Learning Curve and Production Standards: Learning Implications


The phenomenon of learning is a natural characteristic of human activity. For the job participant, learning is an important source of psychological growth; for the organization, learning is a source of increased efficiency and ingenuity [1]. From either perspective, learning is a goal toward which efforts should be directed. Although it is a natural characteristic of human activity, there is a substantial degree of variation possible in how quickly and to what extent learning occurs. To assume that learning will just happen is to fail to understand that learning can be improved and directed to benefit both the individual and the organization.

This article examines the components of the learning curve model from a behavioral perspective. Under this approach, differences in human abilities are considered and incorporated into the model. Conversely, a scientific management approach treats the model as a static standard which depicts learning as an inert process. The behavioral approach emphasizes the effect of learning on the model, while the scientific management approach emphasizes the effect of the model on learning.

Historical Recognition of Learning

The learning curve effect was originally addressed in the literature by T. P. Wright in 1936[17]. He observed that learning normally follows a particular pattern - as additional units are produced, the time required to produce an individual unit decreases at a uniform rate. This effect necessitates the reduction of direct labor hour and cost standards as production progresses.

Researchers during World War II experimented with the learning curve phenomenon in an attempt to predict production costs and time requirements. They found that learning follows a pattern which corresponds to an exponential curve, which is consistent with the intuitive belief that people tend to perform a task more efficiently as they gain more experience - learning enhances efficiency.

Following the war, traditional management practices were expanded based on the belief that the ability to quantify desired performance levels would lead to desired levels of performance. The natural tendency, and possible deficiency, associated with this approach is to model learning ability based on some mathematical model. While empirical data does conform to a mathematical learning curve model, the model alone provides little insight into why or how learning occurs[4]. Thus, the appeal of being able to quantify learning ability often overshadows the importance of comprehending how learning may affect performance.

For example, to calculate the average cumulative hours for the 4th batch: (1) multiply the average cumulative hours for the 2nd batch by the number of units of output in the 4th batch (3.2 * 200 = 640), (2) multiply that product by the 80% learning rate (620 * 80% = 512), (3) divide that number by the total units produced to arrive at the average cumulative hours per unit (512/200 = 2.56).

The application of the learning curve during the early post war years was consistent with other management practices developed during that same time. Job participants, whether controlled by standards, budgets, or the learning curve, were essentially viewed as "passive instruments capable of performing work and accepting directions, but not initiating action or exerting influence in any significant way" [13]. Learning was not perceived to be a natural characteristic of human activity but as an element of a sliding/mechanical norm (the learning curve).

If the learning curve is to be a practical tool, human attributes cannot be ignored. Just as the areas of standard costing and budgeting have had to incorporate behavioral concepts to increase their effectiveness, so must learning curve applications include behavioral considerations[10,16]. In short, quantification of performance expectations does not necessarily guarantee the achievement of those expectations.

Mechanics of the Learning Curve

Before considering the behavioral characteristics of learning, the learning curve model and its mathematical characteristics are examined. Several versions of the model have been proposed[3]. For illustrative purposes, the cumulative average time learning curve model is used in this article. It follows the mathematical power function:

y = a[x.sup.b]

where y = cumulative average time required per unit of output, a = time required for first unit, x = cumulative number of units produced, and b = learning parameter. (See Appendix A for the derivation of b.)

Empirical evidence suggests that the time required to accomplish most tasks diminishes by a constant percentage each time output doubles[5]. Therefore, in order to obtain the best fit of the learning curve using empirical data, a doubling of output is usually specified as the interval over which a constant rate of decline occurs, as illustrated in Table 1.

Table : Table 1

Example of Learning Effects on Output (Based on an 80% Learning Rate)
Batch Number Cumulative Cumulative
Number of Units Hours Hours
 1 50 200 4.00
 2 100 320 3.20
 4 200 512 2.56
 8 400 819 2.05
 16 800 1312 1.64

When plotted on normal graph paper, the curve appears as a descending curvilinear line. However, since a constant rate of change is occurring, if log-log graph paper is used, the learning curve becomes a straight line. As a result, only two points need to be established in order to identify and project the phenomenon of learning. Figure 1 depicts three learning curves plotted using log-log coordinates.

Learning curves A and B require the same time to produce the first unit (a value) but reflect different rates of learning (b value). Learning curve C originates at a lower point on the vertical axis; this implies that less time is required to produce the first unit (smaller a value). Note, however, that learning curves C and A are parallel which indicates that the learning rates are identical. It is important to realize that these three learning curves are not necessarily for different jobs. Depending upon the manner and atmosphere in which learning occurs, any of the three curves could exist for the same job. The recognition of factors that can influence the learning process may provide a better understanding of how the phenomenon of learning can exhibit such flexibility.

Sources of Learning

As a basis for discussion, three areas of learning are examined: (1) preproduction learning, (2) intratask learning, and (3) exoteric learning. This method of classification emphasizes that learning, and therefore the learning curve model, is influenced by factors that emanate from different sources at different times during the production process.

Preproduction Learning. Knowledge acquired before a process starts can be generally described as preproduction learning. The a component in the learning curve model, y = a[x.sup.b], represents this type of learning. The a value, which is the time required to produce the first unit, is directly related to efforts preceding any new task. Examples of this classification of learning include the development of models and prototypes, components testing and experimentation, and employee training and rehearsals.

Individuals involved in this phase of learning are usually characterized as being specialists whose objective is to "get the bugs out." These specialists are naturally in tune with the importance of learning since the essence of their responsibility is to improve or develop a job process. Several field studies have shown that these preproduction activities do improve the initial efficiency of a process[8,12,15].

Intratask Learning. This type of learning occurs during the production process. The b value, the rate of learning index, represents this classification of learning. Examples of encouraging this type of learning are on-the-job training, incentive awards for new ideas, and application of the learning curve to provide values against which actual performance can be compared.

Employees influenced by this type of learning are typically being trained in a new process. These individuals realize learning gains by working faster or more efficiently as a result of their familiarization with a particular job sequence or the manner in which other group members work[7,11,14].

Exoteric Learning. This category of learning derives from sources external to the organization. The effect of this type of learning on the learning curve model may be reflected in both the a and b values. Examples of this source of learning include feedback from trade associations, suppliers, and customers. Learning of this nature has been described as random in the sense that it cannot be planned[12].

Although this source of learning cannot be anticipated, organizations must be in a position to take advantage of this learning when it does occur. Customer suggestion forms and documenting informal channels of communication with salesmen and suppliers represent formal efforts designed to encourage this method of learning. A benefit related to this type of learning is that it often is obtained without cost.

Interaction Effects

These areas of learning are fairly distinct in their origin, but they are interrelated with respect to the effect they can have on the learning curve model. Learning that is achieved from one type will tend to reduce the learning that can be obtained from another. It follows that instruction prior to beginning production, preproduction learning, will decrease the opportunity for the firm to improve its operations during the process. In other words, efforts directed at reducing the time required for the first unit (a value) will tend to reduce the learning available during the process (b value).

Conversely, little or no preproduction training increases the probability that intratask learning will take place and that this learning will occur at a more accelerated rate[12]. The inference here is that emphasis on preproduction factors would lower initial production costs while the application of more learning resources after production commences would increase the rate of cost decreases as production progresses.

Two different learning curves for the same task are depicted in Figure 2. When relative comparisons are made between learning curves A and B, it is possible to identify the tradeoffs made when one type of learning is emphasized over the other. Also, this analysis indicates that time can be a factor in determining which category of learning to stress[6].

The rate at which intratask learning takes place is reflected in the slope of the curve; a more precipitous slope suggests a faster learning rate. The steeper slope of learning curve A implies that intratask learning is taking place more quickly than in B. Note, however, that up to the point at which the curves intersect, learning curve B reflects a lower average production time per unit because the time required to produce the first unit (a value) is less than that needed to produce the initial unit under the conditions in learning curve A.

Production time tradeoffs become important considerations when learning curve analysis is employed. In other words, should emphasis be placed on the preproduction phase of learning or on intratask learning. For example, for learning curve A to be an appropriate course of action, sufficient output must exist to permit the superior learning rate to offset the initial advantage of preproduction knowledge associated with learning curve B.

The type of learning that is to be emphasized will depend upon the nature of the production process and the qualifications of the personnel to be employed[8]. For instance, an operation that is routine and repetitive might require the use of less sophisticated personnel where in-production learning (b value) would be lower. Therefore, greater benefits may be accrued by using specialists to develop the process prior to actual production thus increasing preproduction learning (a value).

Achieving an Atmosphere of Learning

Regardless of the source or category of learning, there should exist an atmosphere that is conducive for learning development. Discovering new ideas or processes is learning in its purest sense and is nurtured in an environment that encourages experimentation. This climate embodies the underlying belief that any process can be improved[9]. If it is acknowledged that all refinements possible have been actualized in a particular process or that additional learning will not be cost effective, then there will be no incentive to experiment and improve a process.

Graphical representation of the learning curve reveals that learning has a tendency to level out as production expands, as shown in Figure 3. This characteristic of the curve is a function of the mathematical properties of the model. These properties reflect the application of a constant rate of decline in learning to a cumulative average that varies inversely with increases in production. As the learning curve begins to level out, it is often assumed that continued learning will not benefit the process. When this presumption is made, a basic or steady-state standard is adopted[2]. The adoption of a steady-state standard could result in a less than accurate prediction of the average time to produce an additional unit. (The difference between the steady-state curve and the actual learning curve is represented by the shaded area in Figure 3). The effect of instituting a basic standard may be to send a signal to personnel that no additional learning is required or anticipated. [Tabular Data Ommited]

However, it must be remembered that the decreasing average time is associated with an ever increasing number of units, as illustrated in Table 2. Note that the absolute change from the preceding average time becomes smaller as production increases, that is, the curve levels out. To accurately ascertain the effect of continued learning on the process, this absolute difference in the average should be multiplied by the total units produced. This calculation will reflect the total time saved from continuing down the learning curve. In this instance, if a basic standard is adopted after unit 16, the application of that standard will overstate the expected time to complete 32 units by 25.6 hours. The consequence of not recognizing these labor savings may be the establishment of inaccurate application rates for direct labor and overhead. This could, in turn, result in a bias toward more favorable variance analyses in these areas than would be appropriate if continued learning rates were anticipated.

The significance of this analysis is that the benefits from learning may be continuous for long periods of time. Learning increases have been known to persist for several years over many thousands of units in production processes. This attribute of learning thus raises doubt as to whether a steady-state standard should ever be adopted. Imposition of a constant standard may result in the curtailment of the learning process with the demonstrated failure to recognize continued time savings and/or product improvement.


The learning curve can be a very useful tool when it is properly applied. The intent of this article has been to suggest that behavioral implications should be considered when the model is used in establishing production standards. This approach recognizes that learning may originate from different sources and may exhibit interrelationships that the mathematical model by itself does not communicate. Further, unlike the mathematical model, a behavioral approach acknowledges that learning is enhanced in an environment that encourages research, experimentation, and continuation of the learning process.

A behavioral approach to learning incorporates human attributes and expectations into the mathematical model. This assimilation permits control without stifling performance. Too often the human element is forsaken when production standards are adopted, and too often the standards are not later modified or adjusted to reflect changes taking place in the process. Human characteristics should shape tools such as the learning curve to render them effective in monitoring and controlling performance. A behavioral approach to learning curve implementation also helps to assure a more realistic and acceptable modeling of the learning process which may have significant implications for employee innovation and morale.


The b value represents an index of the rate of learning experienced once a job or process has begun. The following log transformation is appropriate for solving for b:
 y = [ax.sup.b]
 log y = log a + b * log x

log y - log a = b * log x
 b = log y - log a
 log x

The numerator of the b solution, log y - log a, can also be written log (y/a) which reflects a percentage relationship. If an 80 percent learning curve is appropriate, then log (y/a) becomes log (.80). The denominator, log x, defines the interval over which the rate of learning occurs. If this rate of learning is to occur over doubled quantities than log x becomes log 2. The above descriptions allow the following heuristic to exist for determining the b value.
 b=log (%)
 log 2


[ 1] Andress, F.J. "The Learning Curve As a Production Tool."

Harvard Business Review, January/February 1954, pp. 87-97. [ 2] Baloff, N. and J.W. Kennelly. "Accounting Implications of

Product and Process Start-Ups." Journal of Accounting Research,

Vol. 5, No. 2, Spring 1967, pp. 131-143. [ 3] Belkaoui, A. The Learning Curve: A Management Accounting

Tool. Westport, Connecticut: Quorum Books, 1986. [ 4] Bump, E.A. "Effects of Learning on Cost Projects." Management

Accounting, May 1974, pp. 19-24. [ 5] Camm, J.D. "A Note on Learning Curve Parameters." Decision

Sciences, Vol. 16, 1985, pp. 325-327. [ 6] Cochran, E.B. "Learning: New Dimension in Labor Standards."

Industrial Engineering, January 1969, pp. 38-47. [ 7] Fine, C.H. "A Quality Control Model with Learning Effects."

Operations Research, May/June 1988, pp. 437-444. [ 8] Hancock, W.M. "The Learning Curve." In Maynard, H.B., ed.

Industrial Engineering Handbook. New York: McGraw-Hill

Book Company, 1971, pp. 102-114. [ 9] Heaney, Richard. "The Learning Effect." Australian Accountant,

August 1987, pp. 12-14, 67. [10] Hopwood, A. Accounting and Human Behavior. Englewood

Cliffs, New Jersey: Prentice-Hall, 1976. [11] Joskow, P.L. and G.A. Rozanski. "The Effect of Learning by

Doing on Nuclear Plant Operating Reliability." Review of

Economics and Statistics, May 1979, pp. 161-168. [12] Levy, F. "Adaptation in the Production Process." Management

Science, Vol. XI, April 1965, pp. 136-145. [13] March, J.G. and H.A. Simon. Organizations. New York: John

Wiley and Sons, Inc., 1958. [14] Ng, A.C. "The Learning Curve Phenomenon and Its Implications

for the Accountant." The Australian Accountant, November

1984, pp. 877-881. [15] Pegels, C.C. "On Startup or Learning Curves: Some New

Approaches." Decision Sciences, Vol. 7, No. 4, 1976, pp. 705-713. [16] Schiff, M. and A.Y. Lewin. Behavioral Aspects of Accounting.

Englewood Cliffs, New Jersey: Prentice-Hall, 1974. [17] Wright, T.P. "Factors Affecting the Cost of Airplanes." Journal

of Industrial Engineering, Vol. 12, No. 4, 1936, pp. 122-128.

PHOTO : Figure 1

PHOTO : Figure 2

PHOTO : Figure 3

Nat Briscoe is Assistant Professor of Accounting, University of Arkansas; Stephen Roark is Assistant Professor of Accounting, University of Arkansas.
COPYRIGHT 1991 St. John's University, College of Business Administration
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 1991 Gale, Cengage Learning. All rights reserved.

Article Details
Printer friendly Cite/link Email Feedback
Author:Briscoe, Nat R.; Roark, Stephen
Publication:Review of Business
Date:Mar 22, 1991
Previous Article:The application of expert systems to securities analysis.
Next Article:Gasping for air.

Related Articles
Using volume and economies of scale to benefit long-term productivity.
Purchasing and the Learning Curve: A Case Study of a Specialty Chemicals Business Unit.
Adjustment of commercial trawling effort for Atlantic cod, Gadus morhua, due to increasing catching efficiency.
Testing now runs schools.
Management accounting--decision management: the learning curve equation has a number of applications in the manufacturing sector. Fortunately, the...
Beyond the learning curve.
Introduction to radar target recognition.

Terms of use | Copyright © 2016 Farlex, Inc. | Feedback | For webmasters