Robust control charts based on self-critical estimation process

Shewhart control chart is a basic technique to monitor the state of a process. We observe observations of a group of size four or five in a rational way and plot some statistics (e.g., means and ranges) on the chart. When setting up the control chart, the control limits are calculated based on preliminary 20-40 samples, which were supposedly obtained from stable operating conditions. But it may be hard to believe, especially at the beginning of constructing the chart for the first time, whether the process is stable and hence all samples were generated under the homogeneous operating conditions. In this report we suggest a mechanism to obtain robust control limits under self-criticism. When outliers are present in the sample, we obtain tighter control limits and hence increase the sensitivity of the chart. Examples will be given via simulation study.