The autoregressive T² chart for monitoring univariate autocorrelated processes

In this paper we investigate the autoregressive T² control chart for statistical process control of autocorrelated processes. The method involves the monitoring, using Hotelling's T² statistic, of a vector formed from a moving window of observations of the univariate autocorrelated process. It is shown that the T² statistic can be decomposed into the sum of the squares of the residual errors for various order autoregressive time series models fit to the process data. Guidelines for designing the autoregressive T² chart are presented, and its performance is compared to that of residual-based CUSUM and Shewhart individual control charts. The autoregressive T² chart has a number of characteristics, including some level of robustness with respect to modeling errors, that make it an attractive alternative to residual-based control charts for autocorrelated processes.