Remarks on Bayesian Control Charts

TL;DR

This paper critically examines Bayesian control charts, highlighting that they are not generally optimal due to historical counterexamples, challenging claims of their economic optimality in process monitoring.

Contribution

It clarifies that Bayesian control charts are not universally optimal, referencing historical counterexamples that undermine their assumed optimality in process control.

Findings

Bayesian control charts are not always optimal.

Historical counterexamples demonstrate limitations of Bayesian charts.

Challenges to claims of economic optimality in Bayesian process control.

Abstract

There is a considerable amount of ongoing research on the use of Bayesian control charts for detecting a shift from a good quality distribution to a bad quality distribution in univariate and multivariate processes. It is widely claimed that Bayesian control charts are economically optimal; see, for example, Calabrese (1995) [Bayesian process control for attributes. Management Science, DOI: 10.1287/mnsc.41.4.637] and Makis (2008) [Multivariate Bayesian control chart. Operations Research, DOI: 10.1287/opre.1070.0495]. Some researchers also generalize the optimality of controls defined based on posterior probabilities to the class of partially observable Markov decision processes. This note points out that the existing Bayesian control charts cannot generally be optimal because many years ago an analytical counterexample was provided by Taylor (1965) [Markovian sequential replacement processes. The Annals of Mathematical Statistics, DOI: 10.1214/aoms/1177699796].