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A model for the measurements from a multiple stream process is analysed as a special case of a multivariate control chart by principal components analysis. The principal components meet the objective of partitioning the control problem into statistics that are sensitive to two types of assignable causes. Simple test statistics result and performance analyses are provided.

Principal components are useful for multivariate process control. Typically, the principal component variables are often selected to summarize the variation in the process data. We provide an analysis to select the principal component variables to be included in a multivariate control chart that incorporates the unique aspects of the process control problem (rather than using traditional principal component guidelines).

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.