A new multivariate EWMA scheme for monitoring covariance matrices

Abstract

To monitor covariance matrices, most of the existing control charts are based on some omnibus test and thus usually are not powerful when one is interested in detecting shifts that occur in a small number of elements of the covariance matrix. A new multivariate exponentially weighted moving average control chart is developed for the monitor of the covariance matrices by integrating the classical -norm-based test with a maximum-norm-based test. Numerical studies show that the new control chart affords more balanced performance under various shift directions than the existing ones and is thus an effective tool for multivariate SPC applications. The implementation of the proposed control chart is demonstrated with an example from the health care industry.