Multivariate Process Variability Monitoring Through Projection

Inspired by the recently developed projection chart, such as the U2 chart for monitoring a shift in the multivariate mean, this article proposes a multivariate projection chart for monitoring process variability. In engineering practice, people often build a linear process model to connect the multivariate quality measurements with a set of fixed assignable causes. The column space of the process model naturally provides a subspace for projection and subsequent monitoring and was indeed used as the projection subspace in the recently developed projection control charts for monitoring a shift the mean. For the purpose of monitoring variability, however, we will show that such a projection may not be advantageous. We propose an alternative projecting statistic, labeled as VS, to be used for constructing a multivariate variability monitoring chart. We show, through extensive numerical studies, that the VS chart entertains several advantages over other competing methods, such as its less restrictive requirements on the process model and generally improved detection performance.