Model-based and model-free control of autocorrelated processes

Advances in automated sampling technology have made autocorrelated data commonplace. Positive autocorrelation degrades control charts designed by classical methods. If a correct time-series model of the autocorrelated process is available, many have advocated the use of control charts on the residuals from the model. Using the average run length criterion in an AR(1) model, we show that plotting averages of batches of the raw data can be an effective alternative to plotting residuals. We consider both weighted averages and the simple, model-free approach of arithmetic averages. We compare these statistics to residuals in both Shewhart and cumulative sum (CUSUM) control charts.