Nonparametric likelihood ratio-based EWMA control chart

ABSTRACT

Nonparametric control charts are among the most important tools of statistical process control. Such charts are useful when there is a lack of knowledge about an underlying distribution or its parameters. Most existing nonparametric control charts are used for monitoring location parameters: they may perform poorly when the scale parameters change arbitrarily over time. In this paper, we propose a new nonparametric control chart based on a powerful likelihood ratio test and the exponential weighted moving-average (EWMA) control chart. Its nonparametric property is applied via a consistent series density estimator in the exponential family. The proposed control chart does not require historical reference samples and can be monitored by fixed control limits. The Monte Carlo simulation results show that the proposed control chart performs well in monitoring both mean and variance shifts, especially in monitoring variance or large mean shifts. Furthermore, a real-data example is given to illustrate the effectiveness of the proposed method.

KEYWORDS:

• exponential series density estimator
• nonparametric likelihood ratio
• statistical process control
• EWMA control chart

Acknowledgements

The authors thank the Editor, the Associate Editor and the anonymous referees for their many helpful comments that have resulted in significant improvements to the article. This work is supported by grants from the National Natural Science Foundation of China (No. 12075162) and the VC and VR Key Lab of Sichuan Province.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The data used to support the findings of this study are available from the corresponding author upon request.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China (12075162).

Notes on contributors

Wen Zhong

Wen Zhong holds the BS degree in Mathematics from Sichuan Normal University. Now, she is pursuing the MS degree in statistics with the school of Mathematics, Sichuan Normal University. Her research interests include quality control and statistical process control.

Liu Liu

Pro. Liu is the dean of the College of Mathematics and Physics at Chengdu University of Technology. He is a professor and a doctoral supervisor. He obtained his PhD degree in Mathematics from Sichuan Normal University and his research interests include big data analysis, statistical process control, and medical statistics.

Wu Fan

Fan Wu holds the BS degree in Mathematics from Qingdao University of Science and Technology. Now, He is pursuing the MS degree in statistics with the school of Mathematics, Sichuan Normal University. His research interests include quality control and statistical process control.