A Multivariate Robust Control Chart for Individual Observations

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To monitor a multivariate process, a classical Hotelling's T2 control chart is often used. However, it is well known that such control charts are very sensitive to the presence of outlying observations in the historical Phase I data used to set the control limit. In this paper, we propose a robust Hotelling's T2-type control chart for individual observations based on highly robust and efficient estimators of the mean vector and covariance matrix known as reweighted minimum covariance determinant (RMCD) estimators. We illustrate how to set the control limit for the proposed control chart, study its performance using simulations, and illustrate implementation in a real-world example.