An adaptive thresholding-based process variability monitoring

Abstract

In high-dimensional processes, monitoring process variability is considerably difficult due to the large number of variables and the limited number of samples. Monitoring changes in the covariance matrix of a multivariate process is often used for monitoring process variability under the assumption that only a few elements in the covariance matrix are changed simultaneously from the in-control values. The existing LASSO-based covariance monitoring charts in the high-dimensional settings provide good performance in detecting some shift patterns depending on the prespecified tuning parameter. In practice, control charts that perform reasonably well over various shift patterns are desired when shift patterns are unknown. In this article, we propose a control chart based on an adaptive LASSO-thresholding for monitoring changes in the covariance matrix. The performance of the proposed chart, which is called the ALT-norm chart, is evaluated for various shift patterns and compared with the existing penalized likelihood-based methods. The results show the effectiveness of the proposed chart. Finally, we illustrate the advantages of the ALT-norm chart through simulated and real data from both the semiconductor industry and a high-dimensional milling process.

Keywords:

• adaptive thresholding estimation
• monitoring covariance matrix
• multivariate statistical process control

Additional information

Funding

This publication was made possible by the NPRP award [NPRP 05-563-2-142] and [NPRP-7 - 1040 - 2 - 393] from the Qatar National Research Fund (a member of The Qatar Foundation).

Notes on contributors

Galal M. Abdella

Galal M. Abdella is an Assistant Professor at the Mechanical and Industrial Engineering Department in the College of Engineering, Qatar University. Dr. Abdella is currently the coordinator of the Engineering Management Program at the Mechanical and Industrial Engineering Department, Qatar University. He was awarded his Ph.D. degree in Indusial and Systems Engineering from Wayne State University, Michigan, USA. His research area has always been centered on utilizing mathematics and advanced statistical data analysis for high-dimensional data processing, modeling and simulating rare events, quality data modeling and analysis, and project resource management.

Jinho Kim

Jinho Kim is a Post-Doctoral Researcher in the Department of Mechanical and Industrial Engineering, Qatar University, Qatar. He received his Ph.D. degree in Industrial and Systems Engineering, Rutgers, The State University of New Jersey, and M.S. in Operations Research and Industrial Engineering from the University of Texas at Austin, TX. His research interests include statistical data analysis, statistical quality control, quality data monitoring, and data mining.

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 American Society for Quality (ASQ) in 2016. He also won the Best Ph.D. Student Award and the Tayfur Altiok Memorial Scholarship by Rutgers University. His research interests include statistical process modeling and monitoring, stochastic processes, reliability engineering, data mining, and data analytics.

Khalifa N. Al-Khalifa

Khalifa N. Al-Khalifa is currently the President of College of North Atlantic, Qatar. He is also full Professor in the Industrial Engineering, Mechanical and Industrial Engineering Department, Qatar University. He was awarded his Ph.D. degree in Manufacturing Engineering, University of Birmingham, UK. His research interests focus on Total Quality Management and Quality and Reliability Engineering. He has published over 40 technical publications related to his research interest. Dr. Al-Khalifa is the chair of ASQ Doha-Qatar Local Member Community, and a member of Qatari engineering society. Currently he is managing research funds worth over USD $5,000,000. He is also a supervisor to a number of postdoctoral fellows and Ph.D. and Masters students.

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, NJ. 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. 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 articles. 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.

Abdel Magid Hamouda

Abdel Magid Hamouda is currently the Dean of College of Engineering, Qatar University. He is an active member of a number of International Scientific Committees, professional societies, and standards boards. Dr. Hamouda is a fellow of the Royal Society of Art (FRSA), a senior member of the Institute of Industrial and Systems Engineering (IISE), a member of the Institute of Highway Transportation, UK, and a member of the American Society for Engineering Education (ASEE). Dr. Hamouda has published over 400 articles, of which over 200 are in well-reputed international journals. He has several patents and has edited several conference proceedings. He is currently managing research funds worth over US$4,000,000. He serves on the editorial board of a number of international journals. He and his coworkers have received a number of prestigious awards. Dr. Hamouda was selected by the Organization of Islamic Countries (OIC) as one of the Top 200 scientists within the OIC. In 2010, he was honored with the Takreem Scientific and Technological Achievement Award, one of the highest awards in the Arab world. Also, he won the Qatar University Merit Award for the years 2010 and 2014. Recently, he won the Qatar University Research Excellence Award 2016.

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.