Nonparametric Bayesian approach to the detection of change point in statistical process control

Abstract

This paper gives an intensive overview of nonparametric Bayesian model relevant to the determination of change point in a process control. We first introduce statistical process control and develop on it describing Bayesian parametric methods followed by the nonparametric Bayesian modeling based on Dirichlet process. This research proposes a new nonparametric Bayesian change point detection approach which in contrast to the Markov approach of Chib [6] uses the Dirichlet process prior to allow an integrative transition of probability from the posterior distribution. Although the Bayesian nonparametric technique on the mixture does not serve as an automated tool for the selection of the number of components in the finite mixture. The Bayesian nonparametric mixture shows a misspeci cation model properly which has been explained further in the methodology. This research shows the principal step-bystep algorithm using nonparametric Bayesian technique with the Dirichlet process prior de fined on the distribution to the detection of change point. This approach can be further extended in the multi-variate change point detection which will be studied in the near future.