A Bayesian Sequential Look at u-Control Charts

Abstract

We extend the usual implementation of u-control charts (uCCs) in two ways. First, we overcome the restrictive (and often inadequate) assumptions of the Poisson model; next, we eliminate the need for the questionable base period by using a sequential procedure. We use empirical Bayes(EB) and Bayes methods and compare them with the traditional frequentist implementation. EB methods are somewhat easy to implement, and they deal nicely with extra-Poisson variability (and, at the same time, informally check the adequacy of the Poisson assumption). However, they still need the base period. The sequential, full Bayes approach, on the other hand, also avoids this drawback of traditional u-charts. The implementation requires numerical simulation, and also use of a prior distribution. Several possibilities for both objective and informative priors are explored. We argue that the sequential, full Bayesian uCC is a powerful and versatile tool for process monitoring.