A unified diagnostic framework via symmetrized data aggregation

Abstract

In statistical process control of high-dimensional data streams, in addition to online monitoring of abnormal changes, fault diagnosis of responsible components has become increasingly important. Existing diagnostic procedures have been designed for some typical models with distribution assumptions. Moreover, there is a lack of systematic approaches to provide a theoretical guarantee of significance in estimating shifted components. In this article, we introduce a new procedure to control the False Discovery Rate (FDR) of fault diagnosis. The proposed method formulates the fault diagnosis as a variable selection problem and utilizes the symmetrized data aggregation technique via sample splitting, data screening, and information pooling to control the FDR. Under some mild conditions, we show that the proposed method can achieve FDR control asymptotically. Extensive numerical studies and two real-data examples demonstrate satisfactory FDR control and remarkable diagnostic power in comparison to existing methods.

Keywords:

• Fault diagnosis
• false discovery rate
• variable selection
• symmetrized data aggregation

Acknowledgments

The authors are grateful to the editor, the associate editor, and three anonymous referees for their comments that have greatly improved this paper. The first author is also grateful to Professor Changliang Zou for his brilliant ideas and helpful discussions.

Additional information

Funding

This research was supported by the National Key R&D Program of China (Grant Nos. 2022ZD0114801, 2019YFC1908502, 2022YFA1003703, 2022YFA1003802, 2022YFA1003803) and NNSF of China Grants (Nos. 12071233, 11925106, 12231011, 11931001, 11971247 and 12101398). Ren’s research was also sponsored by Shanghai Sailing Program.

Notes on contributors

Yanhong Liu

Yanhong Liu is a PhD candidate in the School of Statistics and Data Science, Nankai University. She received her Master’s degree in statistics from Nankai University in 2020. Her research interests include high-dimensional inference, change-point detection and outlier identification, and statistical process control. Her research has been published in various refereed journals in statistics, including Canadian Journal of Statistics and Journal of the Korean Statistical Society.

Haojie Ren

Haojie Ren is an assistant professor in the School of Mathematical Sciences, Shanghai Jiao Tong University. She received her BS, MS, and PhD degrees in statistics from Nankai University in 2013, 2016, and 2018, respectively. She then worked as an Eberly Postdoc Fellow in the Department of Statistics, the Pennsylvania State University. Her research interests include online monitoring and diagnosis, high-dimensional inference, change-point detection and outlier identification. Her research has been published in various refereed journals in statistics and industrial engineering, including Journal of the American Statistical Association, Biometrika, and Journal of Quality Technology.

Zhonghua Li

Zhonghua Li is an associate professor of the School of Statistics and Data Science, Nankai University. He received his PhD degree in statistics from Nankai University. His research interests include high-dimensional statistics, change detection and statistical process control. His research has been published in various refereed journals including Technometrics, Journal of Quality Technology, Computers and Industrial Engineering, etc.