An optimal design of ewma control charts based on median run length

Abstract

The in-control run length distribution of an exponentially weighted moving average (EWMA) control chart is highly skewed, hence interpretation based on the average run length (ARL) can be misleading. In addition, the skewness of the run length distribution changes according to the shift in the mean and this presents more difficulty in any interpretation based on ARL. With respect to a run length distribution, the median run length (MRL) is a more meaningful quantity to depend on since interpretation based on MRL is more readily understood. Two methods of computing the MRL of an EWMA chart are examined with emphasis given to the numerical accuracy. An optimal design of EWMA charts based on MRL is proposed and graphs are provided for determining the chart parameters of an optimal EWMA chart. A normal process is assumed.

Keywords:

• Average run length (ARL)
• Normal distribution
• Exponentially weighted moving average
• Statistical quality control

^∗Dr. Gan is Statistical Consultant and Senior Lecturer, Department of Mathematics.

^∗Dr. Gan is Statistical Consultant and Senior Lecturer, Department of Mathematics.

Notes

^∗Dr. Gan is Statistical Consultant and Senior Lecturer, Department of Mathematics.