Sequential quality control in batch manufacturing

The objective of this article is to present an expository overview of our r ecent studies on developing dynamic approaches to quality control in batch manufacturing. The approaches are dynamic in the sense that they are concer ned with finding policies or controls, instead of merely parametric or stat istical designs. In particular, we emphasize identifying certain optimal se quential procedures and revealing their structural properties. We shall rev iew our studies on the following issues: (i) coordination between the inspection-repair of finished products and the ir follow-up services; (ii) coordination between inspection of different component parts in assemb ly 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 programm ing (MDP). We also incorporate into MDP the usage of stochastic comparison techniques, including those based on notions of stochastic convexity and st ochastic submodularity. These properties play a crucial role in revealing t he structures of the policies and in proving their optimality.