Parametric Models of the Learning Curve Effects with Continuous Responses

In general, as a person gets much experience of a certain task, he tends to complete the job more quickly in that he becomes good at the job. This natural phenomenon is called ‘law of diminishing returns’ in economics or the learning curve effects. The learning curve is a graphical representation of the effects. If the elapsed time decreases as time goes by, learning curve is represented as a monotonically decreasing pattern over the time. In this paper, we propose new models for estimating the learning curve effects and provide some useful information on how many trials we need in order to overcome the learning curve (or to become proficient) and how much time he is supposed to spend to complete the job. We adopt some usual cumulative distribution functions (cdf) to capture the shapes of learning curves. We evaluate performance and uniqueness of models proposed here in the simulation.