Sequential quality control in batch manufacturing

The objective of this article is to present an expository overview of our recent studies on developing dynamic approaches to quality control in batch manufacturing. The approaches are dynamic in the sense that they are concerned with finding policies or controls, instead of merely parametric or statistical designs. In particular, we emphasize identifying certain optimal sequential procedures and revealing their structural properties. We shall review our studies on the following issues: (i) coordination between the inspection–repair of finished products and their follow-up services; (ii) coordination between inspection of different component parts in assembly lines; (iii) coordination between inspection and process revision; and (iv) inter-stage coordination (of the inspection processes at different stages, under capacity constraints, and between production and inspection). The basic methodology underlying our approaches is Markov decision programming (MDP). We also incorporate into MDP the usage of stochastic comparison techniques, including those based on notions of stochastic convexity and stochastic submodularity. These properties play a crucial role in revealing the structures of the policies and in proving their optimality.