Bayesian multiple change-point estimation of Poisson rates in control charts

Eectiveness of root cause analysis eorts, following a control chart signal, will be enhanced if there exists more accurate information about the true time of change in the process. In this study, we consider a Poisson process experiencing an unknown multiple number of step changes in the Poisson rate. We formulate the multiple changepoint scenario using Bayesian hierarchical models. We compute posterior distributions of the change-point parameters including number, location, and magnitude of changes and also corresponding probabilistic intervals and inferences through Reversible Jump Markov Chain Monte Carlo methods. The performance of the Bayesian estimator is investigated over several simulated change-point scenarios. Results show that when the proposed Bayesian estimator is used in conjunction with the c-chart, it can provide precise estimates about the underlying change-point scenario (number, timing, direction, and size of step changes). In comparison with alternatives, including Poisson EWMA and CUSUM built-in estimators and a maximum likelihood estimator, our estimator performs satisfactorily over consecutive monotonic and non-monotonic changes. The proposed Bayesian model and computation framework also benet from probability quantication as well as exibility, which allow us to formulate other process types and change scenarios.