Study of average run lengths for supplementary runs rules in the presence of autocorrelation

The basic assumption underlying statistical control chart criteria is that the process measurements are independent and identically distributed over time. However, autocorrelation and other time-series effects occur frequently in application. In this paper, the effects of autocorrelation are investigated for the frequently advocated supplementary runs rules. For both individual control charts based on the moving range and sample standard deviation, using simulation, the impact of autocorrelation for the AR(1) on in-control average run lengths is given.