Monitoring variability and analyzing multivariate autocorrelated processes

Traditional multivariate quality control charts are based on independent observations. In this paper, we explain how to extend univariate residual charts to multivariate cases and how to combine the traditional statistical process control (SPC) approaches to monitor changes in process variability in a dynamic environment. We propose using Alt's ( 1984) W chart on vector autoregressive (VAR) residuals to monitor the variability for multivariate processes in the presence of autocorrelation. We study examples jointly using the Hotelling T-2 chart on VAR residuals, the W chart, and the Portmanteau test to diagnose the types of shift in process parameters.