Rank-based process control for mixed-type data

ABSTRACT

Conventional statistical process control tools target either continuous or categorical data but seldom both at the same time. However, mixed-type data consisting of both continuous and categorical observations are becoming more common in modern manufacturing processes and service management. However, they cannot be analyzed using traditional methods. By assuming that there is a latent continuous variable that determines the attribute levels of a categorical variable, the ordinal information among the attribute levels can be exploited. This enables us to simultaneously describe and monitor continuous and categorical data in a unified framework of standardized ranks, based on which a multivariate exponentially weighted moving average control chart is proposed. This control chart specializes in detecting location shifts in continuous data and in latent continuous distributions of categorical data. Numerical simulations show that our proposed chart can efficiently detect location shifts and is robust to various distributions.

KEYWORDS:

• EWMA
• latent variable
• ordinal attribute level
• standardized rank
• statistical process control

Acknowledgements

The authors would like to thank the Department Editor and two anonymous referees for their many helpful comments that have resulted in significant improvements in this article.

Funding

Tsung's research was supported by the Hong Kong RGC General Research Funds 619612 and 619913. Li's research was supported by the National Natural Science Foundation of China Grant 71402133 and the China Postdoctoral Science Foundation Grant 2014M552464.

Additional information

Notes on contributors

Dong Ding

Dong Ding is an Associate Professor in the School of Management, Xi’an Polytechnic University. She received her Ph.D. from the Hong Kong University of Science and Technology and her B.Sc. from Nankai Univerisity. Her research interests include quality management, statistical process control, monitoring, and diagnosis.

Fugee Tsung

Fugee Tsung is a Professor and Head of the Department of Industrial Engineering and Logistics Management, Director of the Quality and Data Analytics Lab, at the Hong Kong University of Science and Technology. He is a Fellow of the Institute of Industrial Engineers, Fellow of the American Society for Quality, Academician of the International Academy for Quality, and Fellow of the Hong Kong Institution of Engineers. He received both his M.Sc. and Ph.D. from the University of Michigan, Ann Arbor, and his B.Sc. from the National Taiwan University. He is currently a Department Editor of IIE Transactions, Associate Editor of Technometrics, and Editor-Elect of Journal of Quality Technology. He was also the winner of the Best Paper Award awarded by IIE Transactions in 2003 and 2009. His research interests include quality engineering and management to manufacturing and service industries and statistical process control, monitoring, and diagnosis.

Jian Li

Jian Li is an Assistant 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.