Decomposition of <i>T</i> 2 for Multivariate Control Chart Interpretation

Abstract

Multivariate control charts using Hotelling's T2 statistic are popular and easy to use but interpreting their signals can be a problem. Identifying which characteristic or group of characteristics is out of control when the chart signals often necessitates an examination of the univariate charts for each variable. It is shown in this paper that the interpretation of a signal from a T2 statistic is greatly aided if the corresponding value is partitioned into independent parts. Information on which characteristic is significantly contributing to the signal is readily available from this decomposition.