EWMA Control Charts for Monitoring the Mean of Autocorrelated Processes

A standard assumption when using a control chart to monitor a process is that the observations from the process output are independent. However, for many processes the observations are autocorrelated, and this autocorrelation can have a significant effect on the performance of the control chart. This paper considers the problem of monitoring the mean of a process in which the observations can be modeled as an AR(1) process plus a random error. An exponentially weighted moving average (EWMA) control chart based on the residuals from the forecast values of the model is evaluated using an integral equation method. This control chart's performance is compared to the performance of an EWMA control chart based on the original observations, and the effect of process parameter estimation on the control charts is investigated. When the level of autocorrelation is low or moderate, the two EWMA charts require about the same amount of time to detect various shifts; but for high levels of autocorrelation and large shifts, the EWMA chart of the residuals is a little faster.