The Generally Weighted Moving Average Control Chart for Monitoring the Process Median

Abstract

The generally weighted moving average median (GWMA-[Xtilde]) control chart is employed to monitoring the process sample mean/median. From the statistical point of view, the simulation result reveals that the GWMA-[Xtilde] chart outperforms both the EWMA-[Xtilde] chart and the Shewhart-[Xtilde] chart in detecting small shifts of the process sample mean/median. In detecting the startup shifts, the GWMA-[Xtilde] chart is also more sensitive than the EWMA-FIR-[Xtilde] chart. An example is given to illustrate this study. In general, the X¯ charts are sensitive to outliers, and the [Xtilde] charts are outliers-resistant. In this paper, several [Xtilde] charts and X¯ charts are used for comparison. Although the GWMA-[Xtilde] chart performs very well in outliers-resistance, the GWMA-X¯ chart is the best in fast detecting shifts. Therefore, the average quality cost is considered to be a criterion for choosing a control chart with outliers. The Lorenzen-Vance quality cost model is adopted herein. With various sfifts of the process sample mean/median, the average quality costs of control charts are evaluated under some contaminated normal distributions and cost parameters setting. We conclude that, from the economic point of view, the GWMA-[Xtilde] control chart performs best with outliers.

Keywords:

• EWMA charts
• Generally weighted moving average (GWMA)
• Median charts
• Outliers
• Average quality cost