A robust multivariate Shewhart chart for contaminated normal environments

Abstract

Lately, the multivariate setup of control charts, especially the memory-less chart has received less attention of researchers as compared to the univariate setup. However, the multivariate setup is of paramount importance in this big-data era. In this research work, we study the multivariate Shewhart chart for monitoring location parameter by examining the robustness of this scheme with the mean estimator. We also explored the scheme with some other robust parametric estimators in different process environments. The multivariate estimators such as median, midrange, tri-mean (TM), and Hodges–Lehmann (HL) estimators were examined under uncontaminated, location contaminated, variance contaminated, and both location–variance contaminated normal environments. Through a synthetic Monte Carlo simulation and application of the schemes on a real-life dataset, the findings suggest that the proposed estimators outperform the default estimator of the multivariate scheme (mean). The performance measures of comparing these estimators through the charts are the average run length, standard deviation run length, extra-quadratic loss, and relative average run length. The charts resulting from applying the schemes on real-life dataset recorded from glass manufacturing process also buttresses the simulation findings.