An individual-based description of learning within an organization ...

370 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT, VOL. 47, NO. 3, AUGUST 2000An Individual-Based Description of Learning withinan OrganizationDavid A. Nembhard, Member, IEEE, and Mustafa V. UzumeriAbstract—We examine the problem of selecting a model for anindividual-based representation of learning within a population oflearners. Individual-based representations can be used to createdistributions of learning patterns in the workplace. This is analternate theoretical view of learning in organizations wherebyperformance is a unique attribute of each individual within theorganization. Several published learning curve models are fittedto 3874 episodes of individual performance improvement. Weconclude that a three-parameter hyperbolic function outperformsthe other models for this application. This approach providesmanagers with: 1) distributions of between-worker variabilitywith respect to rate of learning, prior learning, and steady-stateproduction rates; 2) A quantitative measure of workforce learningthat can provide information useful for workforce task-assignments;and 3) a methodological framework for selecting a mostpreferred individual model such that workforce distributions maybe constructed and provide such information. Results indicatethat workers perform in a region between the two extremes of fastimprovement to a low level of productivity and slow improvementto a high level of productivity. Also, workers with more priorexperience tend to have a higher steady-state productivity level.Index Terms—Comparative study, learning, performance measurement,productivity.I. INTRODUCTIONLEARNING in organizations has been the subject of considerableresearch for more than a century. Researchershave observed that unit production costs tend to fall with cumulativeoutput and experience, and have formed learning curves(also known as improvement curves, experience curves, or efficiencycurves) to express this relationship. These curves havebeen valuable, for example, in cost control, forecasting, andstrategic planning [4]. During this period, scholars have examinedlearning curves from many perspectives. Psychologistshave studied and modeled individual learning processes [16],while engineers have modeled learning for manufacturing costs[21] and for line balancing of new production runs [8]. Correspondingly,the literature concerning learning curves is vast,covering a wide range of topics. We categorize these topics intotwo broad areas of research.One area of research has centered on the overall implicationsof learning across large organizational units separated by functional,hierarchical, or geographic boundaries. Often referred toManuscript received June 10, 1996; revised January 1, 1998 and October 1,1998. Review of this manuscript was arranged by Department Editor C. Gaimon.D. A. Nembhard is with the Department of Industrial Engineering, Universityof Wisconsin—Madison, Madison, WI 53706-1572 USA (e-mail: nembhard@engr.wisc.edu).M. V. Uzumeri is with the Department of Management, Auburn University,Auburn, AL 36830 USA.Publisher Item Identifier S 0018-9391(00)06635-6.as organizational learning curves, these have allowed managersto examine experiential productivity improvements, transfer ofknowledge between parallel units (e.g., [10]), and the abilityof an organization to retain this knowledge over time (e.g., [2],[10]). These organizational learning curves use data that are aggregatedover many individuals and many processes, and generallyconsist of a series of production output measures in eachorganizational unit based on time or cumulative work. Althoughit is possible to derive some lower level information from aggregateddata (e.g., [4]), it is generally difficult to disaggregateorganizational level learning into smaller organizational unitswhere workplace interventions and changes are actually implemented.It is also difficult to separate the learning effects fromthe effects of other internal and environmental forces. For example,did production costs go down because the workforcelearned to be more efficient or because automation was introduced?Such questions are difficult to address with aggregateddata.We further note that organizational learning curves aremost appropriate for measuring improvements in plantwideproductivity over time. Such measures would be relativelyunrevealing for steady-state systems that exhibit no long-termchanges in productivity. We remark that learning still occursin these steady-state systems, particularly where there existsturnover or redistribution of individuals within the organization.That is, given a reasonably constant turnover rate, new hiresand retrained workers regularly replace experienced workers,resulting in steady-state productivity on an organizationallevel, but learning occurs for the newly assigned workers at theindividual level.Another area of research has examined the microstructure ofthe learning curve for one individual in order to unravel themechanisms by which learning occurs on the individual level.These studies of individual learning curves, which are centeredon the disciplines of psychology, artificial intelligence, and industrialengineering, tended to rely on small, closely monitoredclinical experiments to investigate the fundamental processes bywhich individuals acquire and retain knowledge (e.g., [1], [12],[16]). Many researchers have examined the determination ofa most appropriate mathematical form for individual learning.While most work has centered on the log-linear model (e.g.,[4], [6], [11], [12], [21]), there have been continuing efforts toidentify alternative formulations. Some alternative forms werefound to represent observed behavior better than the log-linearmodel in their respective industrial settings (e.g., [3], [7], [9],[13], [15], [17]). Unfortunately, in order for managers to investigateexperiential improvements in larger organizational unitssuch as teams or departments, it would be necessary to obtain0018–9391/00$10.00 © 2000 IEEE

NEMBHARD AND UZUMERI: INDIVIDUAL-BASED DESCRIPTION OF LEARNING 373data acquisition system. These manual skills involved sewingoperations in which some worker-paced machinery was used,and which required a high level of hand–eye coordination,manual dexterity, and what is perhaps best described as a“hand” for the work.The workers were paid on a piece-rate basis, where eachemployee workstation had its own electronic terminal andbar-code reader. As workers started and finished each unit ofproduction, a bar-code reader recorded time stamped data.At any point during the day, an employee could query theelectronic terminal to determine how much money had beenearned thus far. In order to compare the performance betweendifferent workers, the data should reflect a consistent level ofquality among workers. Although there was no direct measureof quality or waste, worker output quality was maintainedprimarily by the piece-rate method of compensation, whereinworkers were not paid for nonconforming units of production.Workers were highly motivated to maintain the highest level ofquality since nonconforming units would cost workers the timespent on units for which they were not paid. The direct costof wasted materials is considered negligible relative to laborcosts, and is not included in this study.The production performance data are summarized in adatabase that includes every learning episode that occurredduring a one-year period. If any worker in a general class ofassembly embarked on a skill training program during thisperiod, their performance history was recorded in the database.Some workers were new hires, and others were retrainees whowere learning a new skill that may or may not have been relatedto their previous work skill. In total, the database containsmore than 68 000 records involving 3874 new or retrainedworkers on over 30 similar, yet distinct tasks. Early in each ofthe learning episodes, the performance data were summarizedon a daily basis. Later, as the worker moved along the learningcurve, the performance data were reported on a weekly basis.We remark that the overall production level and the overallnumber of worker-hours remained stationary on a quarterlybasis within the system. Learning occurred on an individuallevel, but no true organizational learning took place duringthe study period.IV. LEARNING CURVE MODELSLearning curve models typically represent a dependent variableof production cost in terms of an independent variable ofcumulative production. These models take on various mathematicalforms in order to represent particular learning curve geometries.In this section, we briefly discuss several commonlearning curve models, which originated as aggregate models,individual models, or combined models. Among these are thefollowing.Aggregate Models: log-linear model [20]DeJong’s learning formula [9]S-curve [7]Stanford-B model [3]Levy’s function [15]Individual Models: exponential functions (two and threeparameter) [16]hyperbolic functions (two and three parameter)[16]Combined Models: Pegels’ function [17]Knecht’s model [13]exponential functions (two and threeparameter) [16].The log-linear or conventional learning curve model is thesimplest of these models, and perhaps one of the most widelystudied (e.g., [4], [12], [19]). It is given by the equation, where is the cost of the first unit of production,is the slope of the line on a log–log graph, is the amount ofcumulative production, and is the cumulative average cost ofproduction.The learning formula introduced by DeJong [9],, is designed to incorporatethe proportion of manual work in a man–machine task. Operationsthat are partially paced by machine throughput rates willlimit the ability of the operator to compress the per-unit cycletime. Thus, the model makes use of an incompressibility factor. When , the DeJong model reduces to the log-linearform.The S-curve function [7] is a four-parameter model of theform , where and arethe cost of the first unit and the slope, respectively. Variableis called the equivalent experience units, and the model hasan incompressibility factor, much like the DeJong model. TheS-curve form is based on the assumption that the start up ofthe learning process is more gradual than the log-linear wouldsuggest.The Stanford-B model,, with the inclusionof the parameter, is a superset of the log-linear model. It is aspecial case ( ) of the S-curve model, and was found tobe the best available model for the manufacture of Boeing 707aircraft [3].In order to account for empirically observed phenomena inlearning data, other models were presented by Levy [15], Pegels [17] ,and Knecht [13]. Levy’s function accounts for aleveling off of production rates. Pegels introduced an alternativefunctional form, and Knecht introduced a function that permitsnonconstant slopes in the learning curve when the cumulativeproduction exceeds several hundred units. Each of theselatter three models, however, has shape parameters that are difficultto interpret with respect to learning behavior. By contrast,Mazur and Hastie [16] examined two exponential,, and two hyperbolic,, functionalmodels of learning by individuals for both manual and conceptualskills. The models were hypothesized to represent observedlearning phenomena, and hence have parameter definitions withrelatively straightforward interpretations.We remark that there exist many models of learning in additionto those listed above. We selected a representative subsetof models that are appropriate for the dataset to be examined.These will aid in the examination of the model selection criteriagiven in the section that follows. A different subset of

376 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT, VOL. 47, NO. 3, AUGUST 2000(a)(b)(c)(d)Fig. 3. (a) Example of negative learning by a retrainee. (b) Example of positive learning with high k. (c) Example of high prior learning p. (d) Example of priorlearning and positive learning.[4], [16], [18]). The values for the hyperbolic-3 model areshown in Table II. If the model is suitably fitted to each individual’sperformance history, then the set of workforce learningcurves may be represented by the set of parameter estimates( ) for each individual. We remark that, by plotting each ofthe individual ( )-triplet estimates in 3-space, we can constructa “map” of learning performance within an organizationalunit (e.g., Fig. 4). Such a map provides insight for managerswho can view learning shifts for groups within the workforceafter workplace interventions are implemented. For example, atraining program may not improve the overall average performanceon an organizational level, but may instead improve therate of learning for a subgroup, and result in negative changesin other subgroups.The distributions of the fitted parameter estimates across all3874 learning episodes are shown in Table II. We note that themedian performance limit is only 94% of the current standardvalue of 1.0, indicating that the current work standard might beset above the workforce’s capability. Management may chooseto adjust work standards on the basis of empirical evidence. Fig.4 illustrates pairwise views of the model parameter space for asample task. It is evident from the diagram that the individuallearning curve parameters are distributed in a regular patternacross the workforce. At one extreme, workers start slowly (large

NEMBHARD AND UZUMERI: INDIVIDUAL-BASED DESCRIPTION OF LEARNING 377Fig. 4.Pairwise and 3-D scatter plots for representative task (237 retrainees, 110 new hires).TABLE IICHARACTERISTICS OF FITTED LEARNING CURVES (n =3874)), and eventually attain a high level of productivity (high ).At the other extreme, workers start quickly (small ), yet leveloff at relatively low levels of productivity (low ). At least 10%of the workforce show zero prior experience, and another 10%show significant prior experience. This distribution providesmanagers with the potential to allocate workers, for example,with large to long production runs and workers with small toshorter runs. Higher prior experience workers also tend to havehigher values of and , indicating that they will eventuallyreach a relatively high steady-state level, but will reach it moreslowly than a low prior experience worker. Hence, recruiting andretaining workers who will tend to have high prior experience(e.g., from a competitor) can have benefits for the processes withlong production runs. Learning maps for the other tasks provideanalogous results. However, the amount of variability changedfrom task to task. Between-task variability provides feedback ontask complexity, work standards, and the possible identificationof tasks that are poorly understood by workers.The relative performance values (Table I) indicate that thethree-parameter hyperbolic model has empirical advantages forthis type of analysis. Mazur and Hastie [16] note that, if thehyperbolic function’s limitations are observed, the function iseasily specified, relatively simple to operationalize, and appropriatefor both motor learning and perceptual learning. This conclusionis, however, subject to two important caveats.First, our dataset centered on tasks involving the learning ofmanual dexterity. It is possible that other models will performbetter for different types of learning. However, other studies suggestthat the three-parameter hyperbolic model is robust, withthe potential to model even cognitive learning [16].Second, there is an important distinction between selectingthe model that best fits a single learning episode and choosing a

378 IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT, VOL. 47, NO. 3, AUGUST 2000single model that best fits a large number of individual learningepisodes. With thousands of individual episodes, there arebound to be cases where a different model would provide abetter fit for a specific individual. However, consistently usingonly one functional form allows us to describe a population interms of individuals.VII. SUMMARY AND CONCLUSIONOrganizational learning has been generally measured in aggregate,in such a way that it is difficult to determine a singleindividual’s contribution or how the individual improves overtime. Recent implementations of data acquisition systems makeit increasingly feasible to measure each individual’s learningcurve over time. However, in order to make this informationuseful to managers, there is a need to summarize the informationover larger organizational units. A straightforward summarizationapproach is to plot the parameters from an individuallearning curve model for all of the individual workers within anorganizational unit on a single figure, forming a map of learning.The construction of such a map can be a valuable resource formanagers in evaluating the efficacy of training programs, taskassignment, and reassignments and other plant-floor interventions.In order to create the map we describe, a single individual-basedlearning curve functional form should be selected.Our approach in selecting the functional form was to considermodel selection criteria of efficiency, stability, and parsimony.The three-parameter hyperbolic model had the best empiricalperformance in terms of efficiency and stability. The traditionallog-linear form had only two parameters, one fewer than thethree-parameter hyperbolic function, but was fifth in terms ofefficiency and stability. The log-linear, however, was not suitablefor representing episodes of negative learning. The dataand model allowed us to identify several regular patterns inworkplace productivity improvement. Workers perform in a regionbetween the two extremes of fast improvement to a lowlevel and slow improvement to a high level. In addition, workerswith more prior experience tend to be the workers with a highersteady-state productivity level. These conclusions held acrossall of the tasks involved. We noted that these results are applicableto the specific learning situation from which the data wereobtained, but may also apply to other closely related tasks. Asimilar comparison of models on a broader range of learningsituations is of considerable research interest.REFERENCES[1] J. R. Anderson, “Acquisition of cognitive skill,” Psychol. Rev., vol. 89,no. 4, pp. 369–406, 1982.[2] L. Argote, S. L. Beckman, and E. Epple, “The persistence and transfer oflearning in industrial settings,” Manage. 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Nembhard (M’99) received the Ph.D.degree in industrial and operations engineering fromthe University of Michigan, Ann Arbor, Michiganin 1994, and B.S.E. degree in systems and controlengineering from Case Western Reserve University,Cleveland, Ohio in 1987.From 1994 to 1998 he was assistant professor ofoperations management at Auburn University. From1998 to the present he holds an appointment as AssistantProfessor of Industrial Engineering at the Universityof Wisconsin-Madison.Dr. Nembhard is a member if IEEE, The Institute for Operations Researchand the Management Sciences, and The American Society for Quality.Mustafa V. Uzumeri, photograph and biography not available at the time ofpublication.