Using vector autoregressive residuals to monitor multivariate processes in the presence of serial correlation

Traditional literature on statistical quality control discusses separately multivariate control charts for independent processes and univariate control charts for autocorrelated processes. We extend univariate residual monitoring to the multivariate environment, and propose using vector autoregressive residuals (VAR) to monitor multivariate processes in the presence of serial correlation. We mathematically examine the effects of shifts in process parameters on the VAR residual chart, and give examples using data from a plastic production process. The results indicate the feasibility of VAR residual chart to achieve quality control and improvement.