Robust Location Estimators for the (X)over-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) over 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) over bar phase II control chart limits.