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

A multivariate T² 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 T² 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 T² 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 T² chart.