Causation-based process monitoring and diagnosis for multivariate categorical processes

ABSTRACT

As many manufacturing and service processes nowadays involve multiple categorical quality characteristics, statistical surveillance for multivariate categorical processes has attracted increasing attention recently. However, in the literature there are only a few research papers that focus on the monitoring and diagnosis of such processes. This may be partly due to the challenges and limitations in describing the correlation relationships among categorical variables. In many applications, causal relationships may exist among categorical variables, in which the shifts at upstream, or cause, variables will propagate to their downstream, or effect, variables based on the causal structure. In such cases, a causation-based rather than correlation-based description would better account for the relationship among multiple categorical variables. This provides a new opportunity to establish improved monitoring and diagnosis schemes. In this article, we employ a Bayesian network to characterize such causal relationships and integrate it with a statistical process control technique. We propose two control charts for detecting shifts in the conditional probabilities of the multiple categorical variables that are embedded in the Bayesian network. The first chart provides a general tool, and the second chart integrates directional information, which also leads to a diagnostic prescription of shift locations. Both simulation and real case studies are used to demonstrate the effectiveness of the proposed monitoring and diagnostic schemes.

KEYWORDS:

• Bayesian network
• conditional probability
• contingency table
• directional shift
• statistical process control

Acknowledgements

The authors acknowledge the efforts of the department editor and anonymous referees that have resulted in great improvement of this article.

Funding

Liu's research was supported by the National Natural Science Foundation of China Grants 71402133, 71602155, 11501209, and 71572138, and the Open Fund of State Key Laboratory for Manufacturing Systems Engineering (Xi'an Jiaotong University) sklms2016010. Liu's research was supported in part by the National Science Foundation under Grant CMMI-1362529 and the National Natural Science Foundation of China under Grant 71471005. The authors acknowledge the support of the above grants.

Additional information

Notes on contributors

Jian Li

Jian Li is an associate professor in the School of Management, Xi'an Jiaotong University. He received his Ph.D. from the Hong Kong University of Science and Technology and his B.Sc. from Tsinghua University, Beijing. His research interests include quality management and Six Sigma implementation, statistical process control, and statistical data mining.

Kaibo Liu

Kaibo Liu received a B.S. degree in Industrial Engineering and Engineering Management from the Hong Kong University of Science and Technology in 2009 and an M.S. degree in Statistics and a Ph.D. degree in Industrial Engineering from the Georgia Institute of Technology in 2011 and 2013. Currently, he is an assistant professor at the Department of Industrial and Systems Engineering, University of Wisconsin–Madison. His research interests are focused on data fusion for process modeling, monitoring, diagnosis and prognostics. He is a member of IEEE, ASQ, INFORMS, and IIE.

Xiaochen Xian

Xiaochen Xian received a B.S. degree in Mathematics from Zhejiang University, Hangzhou, China, in 2014. Currently she is a Ph.D. student in the Department of Industrial and Systems Engineering, University of Wisconsin–Madison. Her research interests are focused on high-dimensional monitoring.