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Abstract
When a multivariate control chart raises an out-of-control signal, several diagnostic questions arise. When did the change occur? Which components or quality characteristics changed? For those components for which the mean shifted, what are the new values for the mean? While methods exist for addressing these questions individually, we present a Bayesian approach that addresses all three questions in a single model. We employ Markov chain Monte Carlo (MCMC) methods in a Bayesian analysis that can be used in a unified approach to the diagnostics questions for multivariate charts. We demonstrate how a reversible jump Markov chain Monte Carlo (RJMCMC) approach can be used to infer (1) the change point, (2) the change model (i.e., which components changed), and (3) post-change estimates of the mean.
Additional information
Notes on contributors
Robert M. Steward
Dr. Steward is an Aeronautical Analyst with the National Geospatial-Intelligence Agency. His email is [email protected].
Steven E. Rigdon
Dr. Rigdon is Professor in the Department of Biostatistics. His email is [email protected].
Rong Pan
Dr. Pan is Associate Professor in the School of Computing, Informatics, and Decision Systems Engineering. He is a Senior Member of ASQ. His email is [email protected].