A Multivariate Robust Control Chart for Individual Observations

Abstract

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.

• Hotelling's T²
• Multivariate Robust Estimation of Location and Scatter
• Multivariate Statistical Process Control
• Outliers
• Reweighted Minimum Covariance Determinant Estimators

Additional information

Notes on contributors

Shoja'Eddin Chenouri

Dr. Chenouri is an Assistant Professor in the Department of Statistics and Actuarial Science. His email address is [email protected].

Stefan H. Steiner

Dr. Steiner is an Associate Professor in the Department of Statistics and Actuarial Science. He is a Senior Member of ASQ. His email address is [email protected].

Asokan Mulayath Variyath

Dr. Variyath is an Assistant Professor in the Department of Mathematics and Statistics. His email address is [email protected].