A robust multivariate sign control chart for detecting shifts in covariance matrix under the elliptical directions distributions

Abstract

Most existing control charts monitoring the covariance matrix of multiple variables were restricted to multivariate normal distribution. When the process distribution is non-normal, the performance of these control charts could potentially be (highly) affected, especially for heavy-tail distributions. To construct a robust multivariate control chart for monitoring the covariance matrix, we applied spatial sign covariance matrix and maximum norm to the exponentially weighted moving average (EWMA) scheme and proposed a Phase II control chart. The novel chart is distribution-free under the family of elliptical directions distributions. Comparison studies demonstrate that the novel method is very powerful in detecting various shifts, especially for heavy-tailed distributions. The implementation of the proposed control chart is demonstrated by a white wine data.

Keywords:

• Covariance matrix
• multivariate statistical process control
• robust
• sparsity
• spatial sign test

Acknowledgements

The authors wish to thank the editor, the associate editor and the anonymous referees for numerous insightful comments which improve the paper greatly.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Science Fund of China under [grant number 11501209], [grant number 11771145], [grant number 71772147], [grant number 71602115], [grant number 11571113], [grant number 11471119]; the Postdoctoral Science Foundation of China [grant number 2015M570348], [number 20160089]; Natural Science Foundation of Anhui Province Universities [KJ2017A399]; Natural Science Foundation of Huangshan Universities [2016xkjq007]; the Fundamental Research Funds for the Central Universities and the 111 Project(B14019); the Project of Shanghai Universities to enhance the competition and innovation ‘collaborative innovation of modern statistical methods and theory’.