Year: 2017
Type: preprint
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].
Authors: Ahmadi-Javid, Amir, Ebadi, Mohsen
Institution: Amirkabir University of Technology
Language: English
Subfield: Statistics, Probability and Uncertainty
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2774399348