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ABSTRACT
Many engineering studies for manufacturing processes, such as for quality monitoring and fault detection, consist of complicated functional data with sharp changes. That is, the data curves in these studies exhibit large local variations. This article proposes a wavelet-based local random-effect model that characterizes the variations within multiple curves in certain local regions. An integrated mean and variance thresholding procedure is developed to address the large number of parameters in both the mean and variance models and keep the model simple and fit the data curves well. Guidelines are provided to select the regularization parameters in the penalized wavelet-likelihood method used for the parameter estimations. The proposed mean and variance thresholding procedure is used to develop new statistical procedures for process monitoring with complicated functional data. A real-life case study shows that the proposed procedure is much more effective in detecting local variations than existing techniques extended from methods based on a single data curve.
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Young-Seon Jeong
Young-Seon Jeong is an assistant professor in the Department of Industrial Engineering at Chonnam National University, Gwangju, South Korea. He received his Ph.D. degree from Rutgers University, New Jersey, in 2011. His recent research focuses on statistical decision-making models for monitoring of process control systems in semiconductor manufacturing systems, development of a statistical data mining methodology with diverse applications such as manufacturing systems, and intelligent transportation systems.
Myong K. Jeong
Myong K. Jeong is a professor in the Department of Industrial and Systems Engineering at Rutgers University. His research interests are focused on developing data-mining techniques, process monitoring and control procedures, and optimization techniques for machine learning. His research has been supported by the National Science Foundation, National Transportation Research Center, United States Department of Agriculture, Qatar National Research Fund, Electronics and Telecommunications Research Institute, and various industries. He has been a consultant for Samsung Electronics, ETRI, KISTI, and other companies.
Jye-Chyi Lu
Jye-Chyi Lu received a Ph.D. degree in statistics from the University of Wisconsin, Madison, in 1998. He is currently a professor in the School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta. His current research interests include decision and data analytics, supply chain management, data mining, industrial statistics, and reliability.
Ming Yuan
Ming Yuan is currently a professor in the Department of Statistics, Columbia University.
Jionghua (Judy) Jin
Jionghua (Judy) Jin is a professor in the Department of Industrial and Operations Engineering at the University of Michigan. She received her Ph.D. degree from the University of Michigan in 1999. Her recent research focuses on data fusion and analytics for system monitoring, diagnosis, quality control, and decision making. Her research emphasizes a multidisciplinary approach by integrating applied statistics, machine learning, signal processing, reliability engineering, system control, and decision-making theory. She has received a number of awards, including NSF CAREER and PECASE Awards, and 12 Best Paper Awards since Citation2000. She is an elected Fellow of ASME and IIE; a senior member of ASQ and ISI; and a member of IEEE, INFORMS, and SME.