A Multivariate T~2 Control Chart for Skewed Populations Using Weighted Standard Deviations

摘要

This paper proposes a heuristic method of constructing multivariate T~2 control charts for skewed populations based on 'weighted standard deviations', obtained by decomposing the standard deviation into upper and lower deviations according to the direction and degree of skewness. The proposed method adjusts the variance-covariance matrix of quality characteristics and modifies the ellipsoidal probability density function contour of the multivariate normal distribution to a shape similar to that of the skewed distribution. False alarm rates and out-of-control average run lengths of the proposed control chart are compared with those of the standard control chart for multivariate lognormal, Weibull and gamma distributions, and the results show that considerable improvement over the standard method can be achieved when the distribution is skewed.