Weakly correlated profile monitoring based on sparse multi-channel functional principal component analysis

ABSTRACT

Although several works have been proposed for multi-channel profile monitoring, two additional challenges are yet to be addressed: (i) how to model complex correlations of multi-channel profiles when different profiles have different features (i.e., weakly or sparsely correlated); (ii) how to efficiently detect sparse changes occurring in only a small segment of a few profiles. To fill this research gap, our contributions are twofold. First, we propose a novel Sparse Multi-channel Functional Principal Component Analysis (SMFPCA) to model multi-channel profiles. SMFPCA can not only flexibly describe the correlation structure of multiple, or even high-dimensional, profiles with distinct features, but also achieve sparse PCA scores which are easily interpretable. Second, we propose an efficient convergence-guaranteed optimization algorithm to solve SMFPCA in real time based on the block coordinate descent algorithm. Third, as the SMFPCA scores can naturally identify sparse out-of-control (OC) patterns, we use the scores to construct a monitoring scheme which provides increased sensitivity to sparse OC changes. Numerical studies together with a real case study in a manufacturing system demonstrate the effectiveness of the developed methodology.

KEYWORDS:

• Dimension reduction
• EWMA
• functional PCA
• multi-channel profiles
• sparse PCA
• statistical process control

Acknowledgement

The authors are grateful to the valuable comments provided by the editors and referees.

Additional information

Funding

This project is partially supported by the NSF grant CCF-1740776.

Notes on contributors

Chen Zhang

Chen Zhang received her B.Eng. degree in electronic science and technology (optics) from Tianjin University in 2012, and her Ph.D. degree in industrial systems engineering & management from National University of Singapore in 2017. Currently, she is an assistant professor at the Department of Industrial Engineering, Tsinghua University. Her research interests include developing new approaches for modeling and monitoring of engineering systems with complex data. She is a member of IISE and INFORMS.

Hao Yan

Hao Yan received a B.S. degree in physics from Peking University, Beijing, China, in 2011. He also received an M.S. degree in statistics, an M.S. degree in computational science and engineering, and a Ph.D. degree in industrial engineering from Georgia Institute of Technology, Atlanta, in 2015, 2016, 2017, respectively. Currently, he is an assistant professor in the School of Computing, Informatics, and Decision Systems Engineering at Arizona State University. His research interests focus on scalable machine learning algorithms for large-scale high-dimensional data with complex heterogeneous data structure to extract information or useful features for the purpose of system performance assessment, anomaly detection, intelligent sampling and decision making. He is a member of INFORMS and IISE.

Seungho Lee

Seungho Lee received a B.Eng. degree in industrial engineering from Korea University, an M.S. degrees in industrial & systems engineering from Texas A&M University, and a Ph.D. in systems & industrial engineering from the University of Arizona in 2009. Currently, he is the Principle Engineer in Samsung Electronics. His research areas include multivariable anomaly detection, multistage process analysis, and predictive maintenance.

Jianjun Shi

Jianjun Shi received B.S. and M.S. degrees in electrical engineering from the Beijing Institute of Technology, Beijing, China, in 1984 and 1987, respectively, and a Ph.D. degree in mechanical engineering from the University of Michigan, Ann Arbor, in 1992. Currently, he is the Carolyn J. Stewart Chair Professor in the H. Milton Stewart School of Industrial and Systems Engineering and George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta. His research interests include the fusion of advanced statistical and domain knowledge to develop methodologies for modeling, monitoring, diagnosis, and control for complex manufacturing systems. He is a Fellow of the IISE, a Fellow of ASME, a Fellow of INFORMS, an academician of the International Academy for Quality, an elected member of the ISI, and a life member of ASA.