Bayesian Process Control for Attributes

We consider 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. We show 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. We characterize features of the optimal solution and show 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.