A new Bayesian scheme for self-starting process mean monitoring

ABSTRACT

A self-starting process mean monitoring scheme is needed in applications with short production runs or processes subject to degradation. The major challenge in implementing a self-starting monitoring scheme is that there exists little or no historical in-control data to accurately estimate in-control process parameters. In this paper, we propose a new Bayesian self-starting monitoring scheme to detect on-line whether a process mean has exceeded a pre-determined critical threshold. We assume the process is subject to various types of random drift and random jumps prior to exceeding a critical threshold. In comparison with existing self-starting Bayesian schemes in the literature, our model is more flexible in capturing various types of trends and requires less knowledge of process parameters. In addition, the proposed monitoring scheme is much more computationally efficient, rendering it much more applicable for numerous practical situations where model parameter information is limited and timely detection of a critical event is crucial. Numerical studies based on simulated signals and several real data sets are used to evaluate the performance of the proposed method and compare with existing methods in the literature. The proposed method is shown to be less sensitive to parameter misspecification, more flexible in capturing various trends in the data, and much more computationally efficient.

KEYWORDS:

• Processing Monitoring
• piecewise linear model
• self-starting scheme
• Bayesian method
• particle filter

Acknowledgments

We would like to thank Dr. Nagi Gebraeel of the H. Milton Stewart School of Industrial & Systems Engineering, Georgia Tech University, for kindly providing the bearing degradation data used in the example. The data are collected and owned by Analytics and Prognostics Systems Laboratory at Georgia Tech: http://www.manufacturing.gatech.edu/centers-labs.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research is supported in part by the National Science Foundation under grants [CMMI-1335454 and IIS-1343974] and by the Air Force Office of Scientific Research (AFOSR) [FA9550-14-1-0384].

Notes on contributors

Yuxing Hou

Yuxing Hou is currently a data scientist at Ingram Micro Inc. He received the B.S. in Mechanical Engineering from Huazhong University of Science and Technology, China in 2012, the M.S. in Statistics and Ph.D. in Industrial Engineering, both from the University of Iowa in 2017. His research interests include short-run SPC and novelty detection. He is a member of the INFORMS and the ASA.

Baosheng He

Baosheng He He received the B.S. and M.E. in Electrical Engineering from Xian Jiaotong University, China in 2011 and 2014, respectively. He received Ph.D. in Industrial Engineering from the University of Iowa in 2018. His research interests include short-run SPC and sequential Monte Carlo methods.

Xudong Zhang

Xudong Zhang is currently a Ph.D. candidate in the Department of Industrial and Systems Engineering at the University of Iowa. He received the B. E. degree in mechanics from Zhengzhou University, China in 2013, the M.E. degree in aeronautical engineering from Beihang University, China in 2015, and the M.S. degree in statistics from the University of Iowa in 2018. His Ph.D. research topics include the statistical depth, outlier detection and Bayesian statistical modelling.

Yong Chen

Yong Chen is currently a professor in the Department of Industrial and Systems Engineering at the University of Iowa. He received the B. E. degree in computer science from Tsinghua University, China in 1998, the Master degree in Statistics and Ph. D. degree in Industrial & Operations Engineering, both from the University of Michigan in 2003. His research interests include reliability modeling, novelty detection, process monitoring, diagnosis, and prognosis, and maintenance decision making. He received best paper \s from IIE Transactions in 2004 and 2010. He is serving as an associate editor for Technometrics, IISE Transactions, and Naval Research Logistics. He is a member of the INFORMS, the ASA, and the IMS.

Qingyu Yang

Qingyu Yang received the B.S. and M.S. degrees in automatic control and intelligent system from the University of Science and Technology of China, Hefei, China, in 2000 and 2003, respectively, and the M.S. degree in statistics and the Ph.D. degree in industrial engineering from the University of Iowa, Iowa City, IA, USA, in 2007 and 2008, respectively. He is currently an Associate Professor in the Department of Industrial and Systems Engineering at Wayne State University. Prof. Yang’s research interests include complex sysme diagnosis, reliability analysis, and materials informatics. He is the recipient of the IISE Transactions Best Paper Award in 2011 and the ISERC Best Paper Award in 2009. He is a member of INFORMS and IISE.