A robust \overline {\hbox{X}} control chart based on M-estimators in presence of outliers

Specifying the control limits is an important step in designing a control chart. The control limits are determined by the estimates of mean and/or standard deviation of the process. In the $ \overline {\hbox{X}} $ control chart, when outliers exist in the data, using the classical estimators to estimate parameters may cause the limits to become wider or to shift in the same direction. Robust estimators which are not affected by outliers are used in this research to determine the control limits for $ \overline {\hbox{X}} $ control chart. The mean and the dispersion estimators which are currently applied to define control limits are evaluated, and their performances in control charting are compared with the proposed method by vast simulation and real data examples. Based on the results, it is revealed that when M-estimators with bisquare ρ functions is used to estimate the mean and the dispersion of the process, the control chart has the best performance among the other robust and classical control charts.