Multivariate statistical process control for autocorrelated processes

Abstract

Multivariate statistical process control is often used in chemical and process industries where autocorrelation is most prevalent. We present a realistic model that generates autocorrelation and crosscorrelation and provides a useful approach to characterizing process data. We show how our model relates to the widely-used method of principal component analysis, distinguish between types of assignable causes, and present a useful control statistic based on a principal component decomposition that is not autocorrelated. The control chart for this statistic can be developed by a routine analysis even when the input data is autocorrelated. Furthermore, to characterize our results, we show that any linear combination of the input data that is not autocorrelated is related to our control statistic.