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Learning curves are a useful way of representing the rate of learning over time. Features include an index of baseline performance (y-intercept), the efficiency of learning over time (slope parameter) and the maximal theoretical performance achievable (upper asymptote). Each of these parameters can be statistically modelled on an individual and group basis with the resulting estimates being useful to both learners and educators for feedback and educational quality improvement. In this primer, we review various descriptive and modelling techniques appropriate to learning curves including smoothing, regression modelling and application of the Thurstone model. Using an example dataset we demonstrate each technique as it specifically applies to learning curves and point out limitations. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of the paper is to develop a mathematical model that describes group learning processes with and without worker turnover. Design/methodology/approach – Based on an extensive literature review, fundamental characteristics of group learning processes are first identified and then incorporated into a group learning curve (GLC). The developed GLC is then validated by fitting to empirical data. Findings – The results show that the behaviour of the developed model is in conformance with the characteristics identified in the literature. A comparison with two other learning curves that have frequently been discussed in the literature shows that the GLC developed in this paper is a good mathematical representation of group learning processes. Practical implications – The model developed in this paper enables practitioners to predict performance improvement in groups. Originality/value – The paper is one of the first to propose a mathematical formulation of a GLC. [ABSTRACT FROM AUTHOR]

Abstract: This paper studies the effects of learning and forgetting on a two-stage production system and the position of a potential bottleneck in the system. We start with developing a model for a two-stage serial production system where semi-finished items are fed by the first stage to the second stage, which, in turn, processes the items to their final state. The finished items are transferred either to a subsequent stage or to customers. The paper assumes that both stages of the production system considered are subject to learning and forgetting effects. Learning quickens the production rate as more experience is gained (i.e., when the number of repetitions increases), while forgetting has the opposite effect when production is intermittent (i.e., experience is lost over production breaks). The paper studies how different values of the learning and forgetting parameters influence the ratio of the production rates of both stages and the flow of material in the system. The results of the paper indicate that learning may cause a bottleneck to shift its position in a production system. This happens when an initially slower stage overtakes a previously faster stage over time due to a higher learning rate. The paper thus contributes to the literature on moving bottlenecks and provides practitioners with a model that helps predicting where bottlenecks may arise in the production system, and which enables the system to flexibly react to moving bottlenecks. [Copyright &y& Elsevier]

The economic order (manufacture) quantity model with learning and forgetting has attracted the attention of researchers since the 1960s. All the models developed have limitations, of which two will be addressed in this article. First, the models found in the literature do not address the problem of when the learning exponent b approaches or exceeds the value 1, where these models are mathematically invalid for the special cases of b=1 and 2, and not investigated for the cases 1< b<2 and b>2. Second, the models found in the literature assume that the holding cost per unit is fixed even though the unit production cost is decreasing because of learning. This limitation would suggest producing in smaller lot-sizes than their optimal values. Mathematical models are developed, and existing learning models are revised to overcome these limitations. Numerical examples are presented with results discussed. [ABSTRACT FROM AUTHOR]

Learning associated with mechanical computer-aided design (CAD) poses challenges for both trainers and trainees. This article presents findings that relate to the acquisition of skills in utilizing a modern mechanical CAD tool, Pro/ENGINEER version 2000i2, to design models of low complexity. Empirical learning curves were generated and broken into declarative and procedural components, which were analyzed in an attempt to measure how and how fast trainees developed cognitive and motor skills. Results showed that there is an inverse relationship between the amount of improvement in performance time and the number of build features used in building a solid model. If production time is an overriding criterion, then efforts should be focused on teaching CAD trainees how to build mechanical solid models using small number of complex, more time-efficient features. [ABSTRACT FROM AUTHOR]

This paper studies the effects of learning and forgetting on the production lot size problem with infinite and finite planning horizons. It is assumed that the determination of the economic manufactured quantity (EMQ) in the succeeding production run is dependent on: (1) the maximum inventory accumulated prior to interruption; (2) the length of the interruption period which incurs total forgetting; and (3) the level of experience in equivalent units remembered at the start-up of the next production run. The optimum operating inventory doctrines is obtained by trading off procurement cost per unit time and the inventory carrying cost per unit time, so that their sum will be a minimum. A numerical example is presented to demonstrate the application of learning and forgetting to the determination of the EMQ. [ABSTRACT FROM AUTHOR]

In the above paper, Nembhard and Osothsilp (2001) empirically compared several forgetting models against empirical data on production breaks. Among the models compared was the learn-forget curve model (LFCM) developed by Jaber and Bonney(1996). In previous research, several studies have shown that the LFCM is advantageous to some of the models being investigated, however, Nembhard and Osothsilp (2001) found that the LFCM showed the largest deviation from empirical data. In this commentary, we demonstrate that the poor performance of the LFCM in the study of Nembhard and Osothsilp (2001) might be attributed to an error on their part when fitting the LFCM to their empirical data. [ABSTRACT FROM AUTHOR]