An Improved Distribution-free EWMA Mean Chart

Abstract

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much service data come from a process with variables having nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, should not be properly used here. In this article, we propose an improved asymmetric EWMA mean chart based on a simple statistic to monitor process mean shift. We explored the sampling properties of the new monitoring statistic and calculated the average run lengths of the proposed asymmetric EWMA mean chart. We recommend the proposed improved asymmetric EWMA mean chart because the average run lengths of the modified charts are more accurate and reasonable than those of the five existed mean charts. A numerical example of service times with a right skewed distribution from a service system of a bank branch is used to illustrate the application of the improved asymmetric EWMA mean chart and to compare it with the five existing mean charts. The proposed chart showed better detection performance than those of the five existing mean charts in monitoring and detecting shifts in the process mean.

Keywords:

• Average run length
• Binomial distribution
• Mean chart
• Skewed distribution

Mathematical Subject Classification:

• 62P30
• 62P99

Funding

The research was partially supported by an NSC 100-2118-M-004-003-MY2 research grant, Taiwan, the Commercial College of National Chengchi University, Taiwan and NCTS, Taiwan.