ARL criterion in Bayesian process control using hidden Markov model

In this paper, a multivariate Bayesian control chart is designed for a condition-based maintenance application. The system deterioration process is modeled as a 3-state hidden Markov process, with good, warning and failure states. Bayesian control chart is then applied to monitor the process by plotting the posterior probability that the system is in the warning state. It has been shown in the literature that Bayesian control chart is an optimal tool for statistical process control unlike traditional control charts. In this paper, a new fault detection scheme is developed based on the average run length criterion. Comparison results with former control chart methods are provided to illustrate the effectiveness of this approach.