A theoretical framework and efficiency study of multivariate statistical process control charts

Abstract

A multivariate T ² chart is developed based on the Generalized Likelihood Ratio Test (GLRT) without a priori information about potential mean deviations. Identification of response variables from a T ² chart is challenging and has received considerable attention recently. By highlighting the intrinsic relationship between various multivariate control charts and statistical hypothesis testing, this paper presents a theoretical framework for various individual multivariate control charts including the T ² chart, regression-adjusted chart and M chart. The performance of these control charts is compared under different correlation structures among variables and different mean deviations. A hybrid control chart is also proposed based on the GLRT and union-intersection test, which can serve as a complementary diagnosis tool for the T ² chart.

Keywords:

• Generalized likelihood ratio test
• statistical process control
• T ² test
• union-intersection test

Acknowledgements

The authors would like to thank the department editor and three referees for their valuable suggestions. This work was partially supported by NSF-DMI #0200224. W. Jiang's work was partially supported by NSF-IIS #0542881.