Bayesian Estimation of the Multiple Change Points in Gamma Process Using X-bar chart

The process personnel always seek the opportunity to improve the processes. One of the essential steps for process improvement is to quickly recognize the starting time or the change point of a process disturbance. Different from the traditional normally distributed assumption for a process, this study considers a process which follows a gamma process. In addition, we consider the possibility of the existence of more than one change point. The proposed approach combines the commonly used X-bar control chart with the Bayesian estimation technique using reversible jump Markov chain Monte Carlo method (RJMCMC) to obtain Bayes estimates. The efficiency of our proposed method is evaluated through a series of simulations. The results show that in many cases if there exist more than one change point, our proposed method is able to estimate the true model. Consequently, if there exist more than one change point in the process we have some chance to estimate the true model which will be helpful to determine and remove the root causes introduced into the process. This method is more flexible than the case we assumed that there is just one change point in the process.