Detecting changes in autoregressive processes with X- and EWMA charts

The traditional use of control charts necessarily assumes the independence of data. It is now recognized that many processes are autocorrelated thus violating the fundamental assumption of independence. As a result, there is a need for a broader approach to SPC when data are time-dependent or autocorrelated. This paper utilizes control charts with fixed control limits for residuals to monitor the performance of a process yielding time-dependent data subject to shifts in the mean and the autocorrelation structure. The effectiveness of the framework is evaluated by an average run length study of both X- and EWMA charts using analytical and simulation techniques. Average run lengths are tabulated for various process disturbance scenarios, and recommendations for the most effective monitoring tool are made. The findings of this research present motivation to extend the traditional paradigms of a shifted process (e.g., mean and/or variance). The results show that decreases in the underlying time series parameters are practically impossible to detect with standard control charts. Furthermore, the practitioner is motivated to employ runs rules since the runs are more likely with time-dependent observations.