A Practical Approach for Interpreting Multivariate <i>T</i>² Control Chart Signals

A persistent problem in multivariate control chart procedures is the interpretation of a signal. Determining which variable or group of variables is contributing to the signal can be a difficult task for the practitioner. However, a procedure for decomposing the T2 statistic into orthogonal components greatly aids the interpretation effort. In this paper, a series of examples illustrates the usefulness of this interpretation scheme and relates it to the familiar concept of a statistical distance measure. The relationship between the T2 decomposition procedure and a regression of one variable on a subset of other variables is also demonstrated, and used to aid signal interpretation. Recommendations are made and steps are suggested to provide a faster sequential computation scheme for the decomposition.