Abstract Code: 003-0126
INTEGRATING KNOWLEDGE DEPRECIATION AND KNOWLEDGE TRANSFER INTO THE LEARNING CURVE
Sixteenth Annual Conference of POMS, Chicago, IL, April 29 - May 2, 2005
Ilhyung Kim
College of Business and Economics, WesternWashingtonUniversity
516 High Street, Bellingham, WA98225-9077
, Phone: 360-650-2428, Fax: 360-650-4844
Abstract
Empirical studies show that knowledge acquired from past experience does not persist, but depreciates over time. It is also recognized that knowledge embedded in organizations can be transferred within and among organizations. This paper proposes a learning model, which measures acquisition, depreciation, and transfer of knowledgein a single framework but governed by different rules.The model is applied to a dataset based on the construction of homogeneous ships in sixteen different shipways of a shipyard during World War II. Results indicate that knowledge depreciates rapidly. Only 55% of a stock of knowledge available at the beginning of a month would remain after a month. Results also show that knowledge transfers among the sixteen shipways in the shipyard. The transfer of knowledge occurs not only once at the beginning of a new shipway, but also continuously throughout its life.
(Learning Curve; Knowledge Depreciation; Knowledge Transfer; Empirical Analysis)
1 Introduction
As individuals or organizations repeat a particular task, their knowledge about the task accumulates and as a result the amount of time to complete the task satisfactorilydecreases. This well-known phenomenon is referred to as learning curve or experience-based learning. Since its initial introduction by Wright(1936), numerous theoretical and empirical studies have been conducted on learning curve models. Evidence, supporting the existence of learning curves, has been found in many organizations across various industries. Learning curve models arewidely used to predict production rates and costs, to design training programs, to plan capacity, and to set marketing and manufacturing strategies.
Recently, the reverse of learning– unlearning or depreciation of knowledge - has been recognized and incorporated into the conventional learning models (Bailey, 1989; Globerson et al., 1989; Argote et al., 1990; Darr et al., 1995;Epple et al., 1996; Thompson, 2002; Seo, 2003). Unlearning is a phenomenon that occurs when the amount of knowledge gained from past experience does not persist, but depreciates over time. Simple, personal examples of this unlearning occur when learned foreign languages or mathematics and statistics are not continuously used. It is well known in the psychological literature that depreciationof knowledge (unlearning) and acquisition of knowledge (learning) are governed by quite different laws (Brainerd et al., 1985). This suggests that we develop an integrated learning curve model that captures both learning and unlearning using different rules and assumptions for each of these model components.
Argote, Beckman, and Epple (1990) proposed a model to measure knowledge depreciation in a manufacturing organization. They considered elapsed time as a major predictor for knowledge depreciation. Specifically, they divided the time horizon into a series of discrete time intervals, and explained the knowledge depreciation by measuring the quantity produced in each time interval.Darr, Argote, and Epple. (1995) and Epple, Argote, and Murphy (1996) applied similar models to different situations in other industries. However, their models ignore variations such as interruptions or delays between the tasks in a given time interval.
In order to consider the variations, it is required to monitor the process of each individual unit. Thompson (2002) and Seo (2003) developed models, in which they kept track of the starting and ending times of each individual unit and measured knowledge depreciation based on the elapsed time between two consecutive units. The Liberty ship dataset was used in both studies. Thompson found that knowledge depreciated at the rate of about 2 percent per month in the shipbuilding process, only about one tenth the rate previously reported in Argote et al. (1990). In Seo’s study, depreciation rates were measured for each shipyard and the estimated rates varied from nearly zero (no depreciation) to the rate of 34 percent per month.[1]
It is conceptually understood and empirically supported that knowledge embedded in organizations can be transferred within and among organizations. Zimmerman (1982) and Argote et al. (1990) showed evidence of transfer of learning in the construction of nuclear plants and in the ship-building processes, respectively. This paper examines transfer of knowledge within a single plant. Specifically, it is investigated if knowledge acquired from an existing manufacturing process of a plant is transferred to a newly-installed manufacturing process of the same plant.
Given the above discussion, this paper proposes a learning model, which measuresacquisition, depreciation, and transferof knowledge in a single, integrated framework but governed by different rules. Section 2 reviews the depreciation models in the literature and discusses their limitations. Section 3 proposes a learning model, which incorporatesboth depreciation of knowledge over time and knowledge transfer among different units in an organization. The model is applied to a real dataset of a manufacturing organization, and the empirical results are provided in section 4. Conclusions and directions for future research are presented in section 5.
2 Knowledge Depreciation
The classic learning curve models assume that when a particular task is repeated, the knowledge about the task accumulates and persists over time, i.e., they assume no depreciation of knowledge. However, many experiments and observations show that knowledge may be lost by interruptions, individual forgetting, and simply the passage of time (Baloff, 1970; Bailey, 1989; Globerson et al., 1989).
The dataset of Liberty Ships construction during World War II has been used in many empirical studies of learning due to its special structure.[2]This paper shall use it as well, as it provides a common benchmark to evaluate the various learning (and depreciation) models. Figure 1 shows the production cycle time of Liberty ships built inthe Bethlehem-Fairfield shipyard from April 1941 to October 1944. As shown, we can clearly observe the classic learning curve; namely, as time passes orequivalently cumulative units of production increases, the production cycle time decreases exponentially. We can also observe some abnormal behaviors that cannot be explained by the classic learning curve per se. For example, in December 1942, the production cycle time rose abruptly and then declined. In addition, starting from January 1944, the production cycle time had been gradually rising rather than declining. These patterns could be considered as possible evidence of the occurrence of knowledge depreciation.
FIGURE 1 The Learning Curve of LibertyShipBuilding in Bethlehem-Fairfield Shipyard
[Insert Figure 1 about here.]
To determine the factors which affect knowledge depreciation,Bailey (1989) conducted a laboratory experiment, in which subjects worked at a repetitive manual task in two separate time periods with a break in-between the two periods. In each period the subjects worked for several hours and the breaks ranged from 7 to 114 days. The first period data were used to estimate a commonly-used log-linear learning curve model. The model provided estimated completion times of the tasks for the second period. The difference between the actual time and the learning-curve-estimated time was considered as the “amount of forgetting” attributed to interruption. Moreover, the difference between the initial task time and the learning-curve-estimated time for the first job in the second period was considered as the “amount of learning” prior to interruption. Based on the experiment, Bailey formulated the following regression model with two significant explanatory variables:
,(1)
where D is the amount of forgetting, L is the amount of learning, and B is the length of interruption. As shown in the above equation, forgetting is a function of the amount learned and the elapsed time, not of the learning rate or other variables, which is consistent with the findings in the relevant psychological literature (Brainerd et al., 1985).Bailey’s experiment provides empirical evidence of the existence of forgetting, as well as identifies two important factors which affect such behavior. However, his model cannot explain forgetting thatmay occur without any task interruptions.
Argote et al. (1990) developed a model for estimating the amount of depreciation irrespective of whether or not interruptions occur. Darr et al. (1995) and Epple et al. (1996) applied models similar to Argote et al. (1990) to various situations. Since the structure of these models is identical, we shall limit our discussion to Argote’s model. Their analysis is based on the previously mentioned data from the construction of Liberty Ships built in 16 different shipyards. To capture the effect of depreciation as a function of the elapsed time, they converted the production data into a time series by measuring tonnage produced in each yard in each month. The tonnage produced in each month was estimated by the inputs of labor (labor hours), capital (shipways), and five learning-related variables,which include cumulative output, calendar time (as a surrogate measure of technological change), the rate of new hires, the rate of separations, and the stock of knowledge. Among the five learning-related variables, none of them were significant except the stock of knowledge.The stock of knowledge was assumed to be accumulated by production and at the same time depreciated by a constant rate once in each month. Below is a simplified version of their model showing the structure associated with the stock of knowledge only:
,(2)
where
.(3)
In (2) and (3), qt is tonnage produced in month t and Kt is knowledge acquired through month t. Equation (2) is basically the classic learning curve, in which is referred to as the rate of learning. Equation (3) is a recursive formula portraying knowledge depreciation, in which 1 is considered as the rate of depreciation (0 ≤ ≤ 1). A 95% confidence interval for for the Liberty Ships data is approximately (0.65, 0.85), which implies that only 65% to 85% of the stock of knowledge available at the beginning of each month would remain at the end of the month. Hence, the conventional measure of learning, namely, cumulative output, significantly overstates the persistence of learning.Also, the stock of knowledge and elapsed time were the two important factors affecting depreciation, which is consistent with the results of Bailey’s experiment.
Argote et al.’s model has clearly made contributions to both the theoretical development of the learning curve model and its practical application. However, it has the following potential limitations: (a) the estimates of learning and depreciation rates depend on the length of time period and may result in biased estimates, (b)by itself, it cannot explain the decrease in production quantities (or increase in production cycle times), since the dependent variable qt is a monotonically increasing or decreasing function of time period t,and (c)the model ignores variations within each time interval, due for example to interruptions and breaks.
We now explore theselimitations in more detail.The recursive equation in (3) can be rewritten as:
.(4)
Knowledge acquired through period t, Kt, is a weighted average of past outputs with higher weights given to more recent outputs. The geometric weight given to the output in period i is t-i. Since the model requires an arbitrary length of time period, the weight depends on how the length of the time period is chosen. Thus, the estimate of may be biased.
Both qt and Kt defined in (2) and (3) are monotonically increasing or monotonicallydecreasing in t for all , , and (see Appendix).Hence, the output per period, qt, always increases (or always decreases) over time unless the output in the previous period, qt-1, is lower (or higher) than the level determined in (2). Thus, their model cannot explainper sethe depreciation of knowledge as observed in Figure 1. Argote et al.’s model can be used retrospectively to estimate the rates of learning and depreciation. However,since it is basically an autoregressive model, it cannot explain why the depreciation occurs and what its driving levers are.
Argote et al. converted the actual data into a time series by measuring the amount of production in each period. Even if the amount of production is exactly the same in a given interval, the starting and completion times of each unit in the interval may differ. These variations among the units in an interval are completely ignored in their model. However, as revealed in the relevant literature, elapsed time between works is a critical factor to determine the amount of forgetting (or unlearning). Thus, the variations within a time interval should be considered in order to explain knowledge depreciation, particularly knowledge especially when the variation is large.
On the other hand, Thompson (2002) and Seo (2003) developed models, which consider the variations by monitoring the starting and ending times of each individual unit. Both of their models measured knowledge depreciation based on the elapsed time between two consecutive units. Thompson assumed that knowledge depreciates continuously over time, while Seo assumed it depreciates once in each production unit. Below is a simplified version of their models:
,(5)
where
(6)
In equation (6), tiis timeat which ith unit is produced and is the knowledge retention rate. Note that 1– is the depreciation rate.Equation (5) represents the classic learning curve model. Equation (6) shows how the stock of knowledge accumulates and depreciates over time. Thompson assumed knowledge depreciates continuously over time. In this case, equation (6) can be re-written as follows:
(6)′
Note that in equation (6)′ the retention rate after elapsed time t is
The above models have some advantages over Argote et al.’s model in the following respects: First, the rates of learning and depreciation do not depend on any arbitrary parameters such as the length of time intervals. Thus, the estimates are consistent and unbiased. Second, variations within a time interval are explicitly considered by measuring the elapsed time between the consecutive units. Third, the elapsed time between consecutive units is used as an exogenous variable to explain knowledge depreciation. For the foregoing reasons, this paper adopts a unit-based depreciation model similar to Seo (2003) and Thompson (2002).
3 Model
A learning model is proposed which simultaneously captures acquisition, depreciation, and transfer of knowledge in a single framework. Consider a manufacturing plant which consists of multiple production lines. Each production line operates independently from other lines. Let
MODEL 1:,(7)
where
(8)
and
Yij : Value of the performance measure of ith unit in production line j
Kij : Stock of knowledge available for the production of ith unit in production line j
Sij : Time between the starting time of ith unit and the starting time of (i-1)th unit in production line j
Qij: Cumulative units produced across all production lines before the production of ith unit in production line j
j: Constant in production line j
j : Learning rate in production line j
j: Knowledge retention rate in production line j(Note that 1–j is the depreciation rate.)
: Knowledge transfer rate among the production lines
ij: Error term ofith unit in production line j
Equation (7) represents the classic learning curve model. We use the stock of knowledge as a proxy variable of learning. Transfer of knowledge is allowed among the production lines, as knowledge can be embedded in an organization as a whole and shared by various subunits in the organization. The cumulative number of units produced across all production lines is used as a surrogate measure of the stock of knowledge embedded in the plant to determine the transfer of knowledge among the production lines. Equation (8) shows how the stock of knowledge accumulates and depreciates over time. Figure 2 depicts the process of knowledge acquisition from production and the process of knowledge depreciation over time. The unit of knowledge is defined in such a way that the production of a unit adds one unit of knowledge to its stock. It is well known in the psychological literature that forgetting may be negligible for continuous control tasks such as bicycle riding, but significant for procedural tasks such as computer operation(Bailey, 1989). The model in this paper addresses a procedural task, which is assumed to be continuously divisible, i.e., the task consists of a series of small but different procedures.[3]As defined, the stock of knowledge is Ki-1just prior to the production of the (i-1)th unit. Just after finishing the first small divisible procedure of the(i-1)th unit, the stock of knowledge to be utilized for the same procedure of the next unit is increased by one unit to Ki-1 + 1. However, the stock of knowledge is depreciated before it is utilized for the production of theith unit since Si units of time are elapsed from the starting time of the (i-1)th unit to the starting time of theith unit. Thus, the stock of knowledge available for the production of theith unit, Ki, is determined by, where is the retention rate of knowledge per unit time.Siis used instead of the break time betweenthe two units, Bi, since it is assumed thata procedural task consists of a series of small but different procedures. If there is an interruption between the (i-1)th and the ithunits, Si would be the sum of the production time of the (i-1)th unit and the break time between the two units,Bi. Otherwise, Si would be greater than or equal to the production time of the (i-1)th unit depending on the starting time of the ith unit.
FIGURE 2 Relationship between Acquisition of Knowledge and its Depreciation
[Insert Figure 2 about here.]
The error term ij is assumed to follow a lognormal distribution. The model was estimated using a maximum likelihood criterion. The maximum likelihood estimators of the parameters were determined via nonlinear programming. The maximum likelihood ratio and its asymptoticproperty were used to find the p-values of the test statistics (Casella and Berger, 1990).