Monitoring serially dependent categorical processes with ordinal information

ABSTRACT

In many industrial applications, there is usually a natural order among the attribute levels of categorical process variables or factors, such as good, marginal, and bad. We consider monitoring a serially dependent categorical process with such ordinal information, which is driven by a latent autocorrelated continuous process. The unobservable numerical values of the underlying continuous variable determine the attribute levels of the ordinal factor. We first propose a novel ordinal log-linear model and transform the serially dependent ordinal categorical data into a multi-way contingency table that can be described by the developed model. The ordinal log-linear model can incorporate both the marginal distribution of attribute levels and the serial dependence simultaneously. A serially dependent ordinal categorical chart is proposed to monitor whether there is any shift in the location parameter or in the autocorrelation coefficient of the underlying continuous variable. Simulation results demonstrate its power under various types of latent continuous distributions.

KEYWORDS:

• Autocorrelation coefficient
• contingency table
• location shifts
• ordinal log-linear model
• statistical process control

Acknowledgements

The authors thank the Editor-in-Chief, the Department Editor, and two anonymous referees for their many helpful comments that have resulted in significant improvements in the article.

Additional information

Funding

Dr. Li’s research was supported by the National Natural Science Foundation of China under grants 71772147, 71602155, and 71402133; the National Key R&D Program of China (grant 2016 YFF0202004); and the Major Program of the National Social Science Foundation of China (grant 15ZDB150).

Notes on contributors

Jian Li

Jian Li is an associate professor in the School of Management, Xi’an Jiaotong University, China. He received his B.S. degree in automation from Tsinghua University, Beijing, China, and his Ph.D. degree in industrial engineering and logistics management from the Hong Kong University of Science and Technology, Hong Kong. His current research interests include quality management and quality engineering, Six Sigma implementation, and statistical process control.

Jiakun Xu

Jiakun Xu received her B.S. degree in industrial engineering from the Department of Systems Engineering and Engineering Management at City University of Hong Kong. She is currently a master’s student in the School of Industrial & Systems Engineering at Georgia Institute of Technology. Her research interests include supply chain management and statistical process control.

Qiang Zhou

Qiang Zhou is an assistant professor in the Department of Systems and Industrial Engineering, University of Arizona. He received a B.S. degree in automotive engineering and an M.S. degree in mechanical engineering from Tsinghua University, an M.S. degree in statistics, and a Ph.D. degree in industrial engineering at the University of Wisconsin–Madison. His research interests include modeling, monitoring, and analysis of complex engineering systems for the purpose of quality control and productivity improvement. Dr. Zhou is a member of IEEE, INFORMS, IISE, and ASQ.