Modeling multivariate profiles using Gaussian process-controlled B-splines

Abstract

Due to the increasing presence of profile data in manufacturing, profile monitoring has become one of the most popular research directions in statistical process control. The core of profile monitoring is how to model the profile data. Most of the current methods deal with univariate profile modeling where only within-profile correlation is considered. In this article, a linear mixed-effect model framework is adopted for dealing with multivariate profiles, having both within- and between-profile correlations. For better flexibility yet reduced computational cost, we propose to construct the random component of the linear mixed effects model using B-splines, whose control points are governed by a multivariate Gaussian process. Extensive simulations have been conducted to compare the model with classic models. In the case study, the proposed model is applied to the transmittance profiles from the low-emittance glasses.

Keywords:

• Linear mixed effects model
• multivariate Gaussian process
• B-spline
• profile monitoring

Acknowledgments

The authors are grateful to the anonymous referees for helpful suggestions that improved the presentation of the article.

Additional information

Funding

Zijun Zhang’s research was supported by Hong Kong General Research Fund #11272216.

Notes on contributors

Mithun Ghosh

Mithun Ghosh is a PhD student in the Department of Systems and Industrial Engineering at the University of Arizona. His research focuses on both applied and theoretical aspects of machine learning and data analytics applied to industrial applications. He received his BS degree in the Department of Industrial and Production Engineering, Bangladesh University of Engineering and Technology, Bangladesh.

Yongxiang Li

Yongxiang Li is an assistant professor in the Department of Industrial Engineering and Management, Shanghai Jiao Tong University. He received a PhD in data science from City University of Hong Kong in 2019. His research interests comprise both applied and theoretical aspects of data science integrated with domain knowledge.

Li Zeng

Li Zeng received her BS degree in precision instruments and M.S. degree in optical engineering from Tsinghua University, China, and PhD in industrial engineering and M.S. degree in statistics from the University of Wisconsin-Madison. She is currently an associate professor in the Department of Industrial and Systems Engineering at Texas A&M University. Her research interests are data science and quality engineering in manufacturing and biomedical engineering applications. She is a member of INFORMS and IISE.

Zijun Zhang

Zijun Zhang received his PhD and MS degrees in industrial engineering from the University of Iowa, Iowa City, IA, USA, in 2012 and 2009, respectively, and B.Eng. degree in systems engineering and engineering management from the Chinese University of Hong Kong, Hong Kong, China, in 2008. Currently, he is an associate professor in the School of Data Science at City University of Hong Kong, Hong Kong, China. His research focuses on data mining and computational intelligence with applications in renewable energy, facility energy management, and intelligent transportation domains. He is an associate editor of the Journal of Intelligent Manufacturing.

Qiang Zhou

Qiang Zhou is an assistant professor at the Department of Systems and Industrial Engineering, and a faculty member of the Statistics Graduate Interdisciplinary Programs at University of Arizona. He was an assistant professor at the Department of Systems Engineering and Engineering Management, City University of Hong Kong between 2012 and 2016. His research focuses on advanced industrial data analytics, using statistics and machine learning methods, for engineering decision making and system performance improvement. He is a member of INFORMS and IISE.