The Depletion–Power–Integration–Latency (DPIL) model of spaced and massed repetition

Although several models have been suggested in the literature to describe the relationship between learning and forgetting, this relationship is still not fully understood. This paper proposes the Depletion–Power–Integration–Latency (DPIL) model, which assumes that performing a task repetitively depletes the available encoding resources for that task. The DPIL model fitted five empirical datasets well, reflecting different procedural/episodic learning settings, experimental paradigms (massed/spaced repetition, study time), tests (accuracy, latency), and retention intervals. The model was also fitted to empirical data collected from a quality inspection station at an industrial firm. The DPIL model has the advantage of predicting the length of the final break (interruption) that optimizes performance. This finding is important as it has many industrial engineering applications. The numerical results in this paper show that performance improves as the length of each break preceding the final break increases. This is consistent with empirical findings that moderately short breaks are optimal for performance.

► In this paper, we model how learning interact with forgetting.
► We propose the Depletion–Power–Integration–Latency (DPIL) model.
► DPIL suggest a depletion of encoding resources following repeated training.
► DPIL is applied to several empirical datasets related to industrial settings.
► The model fit data well and moderately long breaks show optimal performance.