Joint diagnosis of process mean vector and covariance matrix for multivariate statistical process control

Abstract

The monitoring methodology in statistical process control is very useful and efficient to detect abnormal changes of a process, however diagnosis ability, accurate fault diagnosis of responsible components for the process change, is limited. Currently, most of work has focused on the diagnosis task of mean shifts. Nevertheless, the shifts of a process also likely occur in the variances/covariances. In this article, we develop a Bayesian procedure to simultaneously diagnose shifts in both mean vector and covariance matrix. Moreover, the proposed method can provide the directions of shifts and corresponding probability. These diagnostic information help decision makers to find quickly root causes of abnormal changes. Compared with existing methods, numerical simulations favor the proposed method. Finally, we use a real dataset from bolt production process to demonstrate the implementation of the proposed Bayesian method.