An efficient charting scheme for multivariate categorical process with a sparse contingency table

Abstract

Multivariate categorical quality characteristics, whose distribution can be displayed by a contingency table, are routinely encountered in many applications. When most of the cell entries in the contingency table are very small or zeros counts, which is so-called sparse contingency table in the literature, existing methods developed in the literature are often inadequate for use, due to the inaccuracy of the maximum likelihood estimate of its probability distribution, and the inflation of online charting statistics. This paper studies the multivariate statistical process control problem for such sparse contingency table. We integrate the group least absolute shrinkage and selection operator (LASSO) method with the Ridge method to estimate the in-control distribution of a contingency table and propose an efficient EWMA control chart, based on a modified Pearson χ² statistic, to monitor the changes in it. Numerical results show that our proposed approach has the best overall performance, compared with its competitors. Finally, a real data example is used to demonstrate the effectiveness of the proposed control chart.

Keywords:

• categorical data
• group LASSO
• log-linear
• multivariate statistical process control
• sparse contingency table

Acknowledgments

The authors greatly acknowledge the efforts of the Editor and three referees that have resulted in great improvements of this paper.

Additional information

Funding

Dr. Xiang's work was supported by the National Natural Science Foundation of China (grants 71931004, 11501209 and 71772147), Natural Science Foundation of Shanghai (grant 19ZR1414400) and the Postdoctoral Science Foundation of China (grants 20160089 and 2015M570348). Prof. Pu's work was supported by National Science Foundation of China Grant (No. 11771145) and the Fundamental Research Funds for the Central Universities and the 111 Project (B14019). Dr. Ding's work was supported by the National Natural Science Foundation of China (grant 71602115). Dr. Liang's work was supported by the National Natural Science Foundation of China (grant 11801210) and the Key program of excellent young talents support plan in Anhui University (grant gxyqZD2019070).

Notes on contributors

Dongdong Xiang

Dongdong Xiang is an associate professor of Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, School of Statistics at East China Normal University. His main research areas are statistical quality control, longitudinal analysis, sequential tests and multiple testing.

Xiaolong Pu

Xiaolong Pu is a professor of School of Statistics at East China Normal University. His main research areas are statistical quality control, design of experiments, sequential tests and reliability.

Dong Ding

Dong Ding is an associate professor of School of Management at Xi'an Polytechnic University. Her main research area is quality control.

Wenjuan Liang

Wenjuan Liang is an associate professor of School of Mathematics and Statistics, Huangshan University. Her main research area is statistical quality control.