A Bayesian Approach to a Process Control Problem

Classical process control methods are not suitable when the number of observations is low. In this study, a Bayesian scheme is considered for a statistical process control problem where process mean is unknown and has jumps in both sides for normal observations. The aim of the study is to detect the changes in the mean for a short-run process. A random walk is defined to indicate the changes of the process mean in time. The posterior distribution of the process mean at time n is found to be a mixture of normal distributions.