Robust location estimators for the X-bar control chart

This article studies estimation methods for the location parameter. We consider several robust location estimators as well as several estimation methods based on a phase I analysis, i.e., the use of a control chart to study a historical dataset retrospectively to identify disturbances. In addition, we propose a new type of phase I analysis. The estimation methods are evaluated in terms of their mean-squared errors and their effect on the X-bar control charts used for real-time process monitoring (phase II). It turns out that the phase I control chart based on the trimmed trimean far outperforms the existing estimation methods. This method has therefore proven to be very suitable for determining X-bar phase II control chart limits.