A control chart based on data depth for monitoring the variability in a multivariate process

Abstract

Majority of the existing statistical procedures for monitoring the covariance matrix of the multivariate processes are based on normality or other distributional assumption. In order to isolate the change in the process variation, these procedures are less powerful due to distributional assumptions. In this article, we study the control charts for monitoring covariance matrix critically. We provide a distribution-free two-sample test for multivariate scale problem called as modified rank test based on data depth. A control chart is proposed based on the data depth based modified rank test. A modified rank test based on data depth is the extension of the modified rank test for univariate two-sample location and scale problem. Data depth based center outward ranking is used for defining test statistic. The performance study of the proposed control charts reveals that the proposed control chart is a better alternative to traditional control charts for variability when a distribution of the process is not known but some historical in-control data is available. The control chart is illustrated with the real-life CSTR process data.

Keywords:

• Average run length
• Data depth
• Multivariate control charts
• Multivariate process
• Nonparametric inference

Acknowledgments

The second author would like to thank Department of Science and Technology, Science and Engineering Research Board, New Delhi for providing financial support under Extra Mural Research scheme [EMR/2017/167] to carry out the research work.