The optimal control limit of a G-EWMAG control chart

Abstract

The control chart is a widely used statistical process control tool that detects any process change and plays an important role in high-quality processes. In this paper, we design G-EWMAG control chart which is sensitive to both small and large shifts. G-EWMAG control chart combines G control chart with EWMAG control chart. The G control chart is based on a plot of the G statistic designed for quality control using attribute data. There is a drawback in G control chart. When it is applied to high-quality processes, it performs poorly in detecting small shifts. On the other hand, EWAMG control chart which apply the EWMA technique with attribute data to G statistics can quickly detect small shifts. G-EWMAG control chart have the alpha ratio which represent the combination ratio of G control chart and G-EWMAG control chart. A large alpha ratio makes the G-EWMAG control chart sensitive to detecting large shifts. On the other hand, a small alpha ratio makes it sensitive to detecting small shifts. But problems arise when the G-EWMAG control chart has an alpha ratio of 1. In this case, a slight numerical difference in average run-length between EWMAG and G-EWMAG appears to exist when detecting small shifts. We suggest optimal control limits for designing the G-EWMAG control chart which is sensitive both large and small shift for use in high-quality processes.