Effect of warning limits on the performance of the X chart under autocorrelation

X charts for variables are one of the outstanding charts of statistical quality control (SQC), used to detect larger shifts in the process mean. In actual practice, many processes are autocorrelated and if these charts are used, their performance is deteriorated. The performance of the chart is measured in terms of the average run length (ARL), which is the average number of samples before getting an out‐of‐control signal. The ARLs at various sets of parameters of the X chart are computed by simulation, using MATLAB. An attempt has been made to counter autocorrelation by designing the X chart using warning limits. Various optimal schemes are proposed for different levels of correlation (Φ). Moreover these optimal schemes of modified X chart are compared with Derman‐Ross's (Derman and Ross, 1997) and Klein's (2000) schemes at various levels of correlation (Φ). It is concluded that the modified X scheme outperforms the Derman‐Ross's (2 of 2) scheme.