Statistical attributes of the power learning curve model

A learning curve is a well known tool which describes the relation between the performance of a task and the number of repetitions of that task. A learning curve model may be used as a prediction tool in various applications of operations planning and control. Previous models have treated learning as a deterministic phenomenon, whereas this paper addresses its stochastic nature and treats learning as a random process. Exact expressions of the variance, of the coefficient of variation and of the probability density function of the performance, expressed as a function of the number of repetitions of a task, are derived for the power model. Mathematical analysis reveals that the coefficient of variation is independent of the number of repetitions. The probability density function type was also found to be independent of the number of repetitions. Analysis of actual learning data validated the theoretical findings. These findings enable improved forecasting of future performance by using a stochastic rather than a deterministic estimation.