The industrial learning curve is the widely observed process whereby, through manufacturing experience, improvement in quality metrics improve over time. Such quality metrics include cost, mean product lifetime, and error rate.

This dissertation motivates, builds, describes, and investigates a learning curve model based on ideas of information theory and statistical mechanics. We first examine the relationship between the learning curve and learning in other contexts. Then we create a model of the learning curve based upon the ideas of statistical mechanics. We then build two continuous models for the learning curve. Several additional features of learning curves, such as multi-dimensional learning and forgetting, are realized by the model.

The first continuous model is based on a new mathematical concept: weak convergence of sequences of sets. The idea of weak convergence of sequences of sets is developed for both deterministic and random sets. Several functional analytic-like results are then proven for such weak limits. The weak limits are then used to construct a model of learning. In doing so, the general approach of creating a continuous model from a discrete model via such a weak limit is described.

The second continuous model to be described is a partial differential equation model. By making the learning process Poisson in time, it is shown that the learning model is a discretization of a transport equation. Aspects of this transport equation are then explored and interpreted.

Further, some simulations of the model are made. It is shown that the model simulations generate the generally observed form of the learning curve. The dissertation concludes with an exploration of further directions to be pursued in future investigation of the learning curve phenomenon.