Effect of autocorrelation estimators on the performance of the X̄ control chart. Issue 13 (2nd September 2018)

• Record Type: Journal Article
• Authors: Garza-Venegas, J. A.; Tercero-Gómez, V. G.; Lee Ho, L.; Castagliola, P.; Celano, G.
• Is Part Of: Journal of statistical computation and simulation. Volume 88:Issue 13(2018)
• Page Start: 2612
• Page End: 2630
• Publication Date: 2018-09-02
• Subjects: AR(1) process -- X¯ control chart -- estimated parameters -- standard deviation of the ARL -- guaranteed performance; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2018.1479752
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: 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 the standard deviation of the ARL ( AARL and SDARL, respectively) are used as performance measures as they summarize the variation due to the Phase I estimations. Considering these performance measures, the effect of several autocorrelation estimators on theX ¯ chart performance was investigated in case of stationaryA R ( 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 ARL 's.