Effect of autocorrelation estimators on the performance of the Xbar control chart

Control charts are powerful Statistical Process Monitoring tools to detect departures from in-control situations. However, their power detection relies on the fact that all assumptions underlying their design are met, such as independence of data and knowledge of the process model parameters. When parameters are estimated, the Average and Standard Deviation of the ARL, (AARL and SDARL, respec- tively) are used as performance measures as they summarize the variation due to the Phase I estimations. Considering these performance measures, the effect of sev- eral autocorrelation estimators on the X chart performance was investigated in case of stationary AR(1) processes . Further, a bootstrapping technique was developed to adjust the corresponding control limits and obtain a guaranteed ARL performance. The effect on the out-of-control ARL due to this adjustment is also presented. Results show that overestimation of the autoregressive parameter leads to higher values of both in-control and out-of-control ARLs