Principal components for diagnosing dispersion in multivariate statistical process control

We provide an easily implemented procedure to help data analysts systematically diagnose which quality characteristics may be driving the dispersion of a multivariate process out of control. Multivariate statistical process control commonly uses Hotelling's T² statistic to indicate when a multivariate observation goes out-of-control. Several techniques currently exist that accurately diagnose which specific variables are driving the T² statistic out-of-control. For subgroups of independently and identically distributed multivariate normal observations, we advocate decomposing the overall T² into independent T² statistics for separate monitoring of location and dispersion. We propose a procedure based on principle components to diagnose the specific variables responsible for driving subgroup dispersion out-of-control. The procedure is demonstrated on a publicly available data-set.