The use of principal components and univariate charts to control multivariate processes

Abstract

In this article, we evaluate the performance of the T² chart based on the principal components (PC X chart) and the simultaneous univariate control charts based on the original variables (SU charts) or based on the principal components (SUPC charts). The main reason to consider the PC chart lies on the dimensionality reduction. However, depending on the disturbance and on the way the original variables are related, the chart is very slow in signaling, except when all variables are negatively correlated and the principal component is wisely selected. Comparing the SU , the SUPC and the T² charts we conclude that the SU X charts (SUPC charts) have a better overall performance when the variables are positively (negatively) correlated. We also develop the expression to obtain the power of two S² charts designed for monitoring the covariance matrix. These joint S² charts are, in the majority of the cases, more efficient than the generalized variance chart.