Joint Diagnosis of High-Dimensional Process Mean and Covariance Matrix based on Bayesian Model Selection

Apart from the quick detection of abnormal changes in a process, it is also critical to pinpoint faulty variables after an out-of-control signal. The existing diagnostic procedures mainly focus on the diagnosis of changes in the process mean. This article investigates the joint diagnosis of high-dimensional process mean and covariance matrix based on Bayesian model selection with nonlocal priors. The proposed procedure enjoys two promising features. First, in addition to the isolation of shifted components, it can also provide a probability that the identified components are true, which is very useful for elimination of root causes of abnormal changes. Second, it possesses the model consistency property in the sense that the probability of identifying the true components with shifts approaches one as the sample size increases. The performance comparisons favor the proposed procedure. A real example based on the urban waste water treatment process is provided to illustrate the implementation of the proposed method.