The Generally Weighted Moving Average Median Control Chart

A generally weighted moving average median (GWMA-X̃) control chart for monitoring the process sample median is proposed. In contrast to the mean control charts, the median control charts are outlier-resistant and are easier to do on the shop floor. Developing an effective median control chart for monitoring the small shifts of the process sample median has the practical necessity. When the adjustment parameter α = 1, the GWMA-X̃ control chart reduces to the EWMA-X̃ control chart. When the design parameter q = 0, the EWMA-X̃ control chart reduces to the Shewhart-X̃ control chart. The properties and design strategies of the GWMA-X̃ control chart are investigated. The numerical simulation is used to evaluate the average run lengths of the GWMA-X̃ control chart, the EWMA-X̃ control chart and the Shewhart-X̃ control chart. After an extensive comparison, it reveals that the GWMA-X control chart outperforms both the EWMA-X̃ control chart and the Shewhart-X̃ control chart in detecting small shifts of the process sample median. An example is also given to illustrate this study.