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.

Keywords:

• change in covariance matrix
• exponentially weighted moving average
• sparsity

Acknowledgments

The authors would like to thank the Editor, Associate Editor and anonymous referees for their many helpful comments that have resulted in significant improvements to this paper.

Notes

Fugee Tsung’s research was supported by RGC Competitive Earmarked Research (Grants 620010 and 619612). Changliang Zou’s research was supported by National Natural Science Foundation of China (Grants 11101306, 11001138, and 70931004), Foundation for the Author of National Excellent Doctoral Dissertation of PR China (Grant H0512101), and New Century Excellent Talents in University (Grant NCET-12-0276).

1. http://archive.ics.uci.edu/ml/datasets/Cardiotocography