Bayesian Multiple Change Point Estimation of Poisson Rates in Control Charts


1 Epidemiology, Executive Medical Services, Western Sydney Local Health District, Sydney, Australia

2 School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

3 Department of Industrial Engineering, Islamic Azad University-Science and Research Branch, Tehran, Iran

4 Discipline of Mathematical Sciences, Science and Engineering Faculty, Queensland University of Technology, Brisbane, Australia


Effectiveness of root cause analysis efforts, following a control chart signal, will be enhanced if there exist more accurate information about the true time of the change in the process. In this study, we consider a Poisson process ex- periencing an unknown multiple number of step changes in the Poisson rate. We formulate the multiple change point 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 investi- gated 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 benefit of probability quantification as well as flexibility which allows us to formulate other process types and change scenarios.