Bayesian process control for attributes

The paper considers a process control procedure with fixed sample sizes and sampling intervals where the fraction defective is the quality variable of interest, a standard attributes control chart methodology. It shows that relatively standard cost assumptions lead to formulation of the process control problem as a partially observed Markov decision process, where the posterior probability of a process shift is a sufficient statistic for decision making. The paper characterizes features of the optimal solution and shows that the optimal policy has a simple control limit structure. Numerical results are provided which indicate that the procedure may provide significant savings over non-Bayesian techniques.