ROBUSTNESS OF MULTIVARIATE CONTROL CHARTS TO NORMALITY ASSUMPTIONS AND OUTLIERS IN THE COVARIANCE MATRIX

We propose a new multivariate Shewhart control chart based on grouped observations for monitoring changes in the covariance matrix. The proposed chart is obtained by applying logarithms to eigenvalues derived through the singular value decomposition of processs covariance matrix. This method allows the proposed chart to be robust to nonnormality in the multivariate datas underlying distribution. We investigate the effect of Phase I outliers on the performance of the proposed chart by using the minimum volume ellipsoid (MVE) estimator. The MVE is one of the most effective robust estimators for detecting outliers in the process covariance matrix. We compare the performance of the introduced chart with the most relevant competitors using average of the conditional average run length based on Phase I parameters estimates. The introduced chart is shown to be more robust to normality assumptions and Phase I outliers than its counterparts. We apply an industrial dataset to support the simulation studies.