A penalized likelihood-based quality monitoring via L₂-norm regularization for high-dimensional processes

Abstract

Technological advances have resulted in the introduction of new products and manufacturing processes that have a large number of characteristics and variables to be monitored to ensure the product quality. Simultaneous monitoring of variables under such a high-dimensional environment is quite challenging. Traditional approaches are less sensitive to the out-of-control signals in high-dimensional processes, especially when only a few variables are responsible for abnormal changes in the process output. Recently, variable selection-based charts are proposed to overcome the drawbacks of the traditional approaches. These approaches adopt diagnosis procedures to identify a small subset of potentially changed variables. However, the detection capability of these charts may be low in cases when the size of the shift is relatively small in a highly correlated data structure, which is critical in modern industry. Moreover, the complexity of computation would dramatically increase as the dimension of the process parameters increases due to the diagnosis procedure, which is inappropriate for online monitoring. This article proposes a new penalized likelihood-based approach via $L_2$ norm regularization, which does not select variables but rather “shrinks” all process mean estimates toward zero. A closed-form solution of the proposed approach along with probability distributions of the monitoring statistic under null and alternative hypotheses are obtained, which makes the proposed chart significantly efficient to monitor high-dimensional processes. In addition, we explore theoretical properties of the approach and present several extensions of the proposed chart and its integration with other existing charts. Finally, we compare the performance of the approach with existing methods and present a case study of a high-speed milling process.

Keywords:

• high-dimensional processes
• penalized likelihood
• ridge regression
• statistical process control
• variable selection

Additional information

Notes on contributors

Sangahn Kim

Sangahn Kim is an Assistant Professor in the Department of Business Analytics and Actuarial Science, Siena College, New York. He received his Ph.D. degree in Department of Industrial and Systems Engineering, Rutgers University, New Jersey. He is a recipient of the Richard A. Freund International Scholarship by the American Society of Quality (ASQ) in 2016. He also won the Tayfur Altiok Memorial Scholarship and the Best PhD Student Award in 2017 by Rutgers University. His research interests include statistical process modeling and monitoring, reliability engineering, data mining, stochastic processes, and data analytics. Email: [email protected]

Myong K. (Mk) Jeong

Myong K. (MK) Jeong is a Professor in the Department of Industrial and Systems Engineering and RUTCOR (Rutgers Center for Operation Research), Rutgers University, New Brunswick, New Jersey. His research interests include data mining, quality and reliability engineering, stochastic processes, and sensor data analysis. He received the prestigious Richard A. Freund International Scholarship by ASQ in 2002 and the National Science Foundation (NSF) CAREER Award in 2002 and 2007, respectively. His research has been funded by the NSF, United States Department of Agriculture (USDA), National Transportation Research Center, Inc. (NTRCI), and industry. He has been a consultant for Samsung Electronics, Intel, ETRI, and other companies. He has published more than 90 refereed journal papers. He has served as an Associate Editor of several journals, such as the IEEE Transaction on Automation Science and Engineering, International Journal of Advanced Manufacturing Technology, and International Journal of Quality, Statistics and Reliability. Email: [email protected]

Elsayed A. Elsayed

Elsayed A. Elsayed is a Distinguished Professor in the Department of Industrial and Systems Engineering, Rutgers, The State University of New Jersey. His research interests are in the areas of quality and reliability engineering. He is the author of Reliability Engineering, John Wiley & Sons, 2012. He is the author and coauthor of work published in IIE Transactions, IEEE Transactions, and the International Journal of Production Research. His research has been funded by the DoD, FAA, NSF, and industry. Dr. Elsayed has been a consultant for DoD, AT&T Bell Laboratories, Ingersoll-Rand, Johnson & Johnson, Personal Products, AT&T Communications, Ethicon, and other companies. Dr. Elsayed was the Editor-in-Chief of IIE Transactions and the Editor of IIE Transactions on Quality and Reliability Engineering. He is also an Editor for the International Journal of Reliability, Quality and Safety Engineering. Email: [email protected]