A heuristic threshold policy for fault detection and diagnosis in multivariate statistical quality control environments

In this paper, a heuristic threshold policy is developed to detect and classify the states of a multivariate quality control system. In this approach, a probability measure called belief is first assigned to the quality characteristics and then the posterior belief of out-of-control characteristics is updated by taking new observations and using a Bayesian rule. If the posterior belief is more than a decision threshold, called minimum acceptable belief determined using a heuristic threshold policy, then the corresponding quality characteristic is classified out-of-control. Besides using a different approach, the main difference between the current research and previous works is that the current work develops a novel heuristic threshold policy, in which in order to save sampling cost and time or when these factors are constrained, the number of the data gathering stages is assumed limited. A numerical example along with some simulation experiments is given at the end to demonstrate the application of the proposed methodology and to evaluate its performances in different scenarios of mean shifts.