Sequential process control under capacity constraints

We consider a sequential process control model under inspection capacity constraints. A 2-state production process observed imperfectly by inspection with general costs and distribution functions is studied. The objective is to develop implementable control policies deciding at each decision epoch whether to produce items without any action, to inspect items, or to repair the process as well as satisfying inspection capacity constraints. The problem is formulated as a Markov decision process using the Bayesian approach. We characterize the features of an unconstrained problem and show that a constrained problem can be transformed to an unconstrained problem. A simplified process control policy is proposed, and numerical examples are presented which indicate that the approximate policy may provide very close results compared with the optimal policy in terms of total operation costs.