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

Abstract

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.

KEYWORDS:

• Bayesian model selection
• Fault isolation
• High-dimensional
• Nonlocal density

Supplementary Materials

Technical details:The PDF file provides the technical details, tables for simulation studies and the attributions of a real dataset as referred in the article. (PDF file)

Source code:The zipped package contains R code and a real dataset for the Section 4 of Simulation Studies and the Section 5 of A Real Data Example. (ZIP file)

Acknowledgments

The authors are very grateful to the editor, associate editor, and anonymous referees for their valuable comments and constructive suggestions that improve the quality of this work significantly.

Additional information

Funding

The work of Dr. Xu was funded by the Guangxi Natural Science Foundation Program (2021GXNSFBA220013) and the Doctoral Research Foundation of Guilin University of Technology (GUTQDJJ2020119). The work of Dr. Shu was funded by the Science and Technology Development Fund of Macau SAR (FDCT/0033/2020/A1), the Department of Science and Technology of Guangdong Province (EF020/FBA-SLJ/2022/GDSTC), and the University of Macau Research Committee (MYRG2022-00017-FBA). The work of Dr. Li was funded by National Natural Science Foundation of China (72072114).