Contributors to a multivariate statistical process control chart signal

A significant practical disadvantage of multivariate statistical process control is that it is difficult to determine which of the monitored variables is responsible for the out-of-control signal. While there have been several proposed techniques and diagnostics, most of these have disadvantages. Rather than an ad hoc selection, we use three approaches to develop a diagnostic for a chi-square chart and generate the same statistic from each approach. Consequently, intuitive interpretations of the diagnostic are provided and previous proposals are simplified by a focus on a single metric.