The quality control chart for monitoring multivariate autocorrelated processes

Previously, quality control and improvement researchers discussed multivariate control charts for independent processes and univariate control charts for autocorrelated processes separately. We combine the two topics and propose vector autoregressive (VAR) control charts for multivariate autocorrelated processes. In addition, we estimate AR(p) models instead of ARMA models for the systematic cause of variation. We discuss the procedures to construct the VAR chart. We examine the effects of parameter shifts and by example present procedures to show the feasibility of VAR control charts. We simulate the average run length to assess the performance of the chart.