Nonparametric multivariate statistical process control charts: a hypothesis testing-based approach

Abstract

Nonparametric multivariate control charts are highly sought-after due to their flexibility to adapt to different distribution assumptions. However, most existing nonparametric multivariate control charts involve some tuning parameter, which needs to be pre-specified to implement those control charts. To choose the appropriate tuning parameter to achieve optimal performance, it usually requires the information about the out-of-control distribution. However, in practice, it is rarely known in advance what the out-of-control distribution is. In this paper, we propose a new nonparametric multivariate phase-II control chart using a hypothesis testing-based approach when a body of reference data (phase-I data) is available. The proposed control chart does not depend on any tuning parameter, and can be considered as a natural generalisation of the generalised likelihood ratio chart to the nonparametric setting. Our simulation study and real data analysis show that the proposed control chart performs well across a broad range of settings, and compares favourably with existing nonparametric multivariate control charts.

Keywords:

• generalised likelihood ratio chart
• hypothesis testing
• nonparametric procedure
• spatial sign
• statistical process control

Acknowledgments

We thank the editor, the associate editor, and the referees for their constructive comments, which have helped improve our paper.

Disclosure statement

No potential conflict of interest was reported by the authors.