A Bayesian approach to diagnostics for multivariate control charts

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.