Average Run Length Performance of Shewhart Control Charts with Interpretation Rules

Abstract

The most popular tool used in the industry for monitoring the process mean is the Shewhart control chart. The major disadvantage of the Shewhart control chart is that it is not very efficient in detecting the small changes in the process mean. In order to make the Shewhart chart more efficient to detect the small changes in the process mean additional interpretation rules has been suggested. In this paper, the average run length (ARL) performance of most used seven interpretation rules were obtained by developing a spread sheet for normal and gamma distributions. The results show that the in-control average run length performance (when process is in control) be fairly high for particular rules when underlying data from a gamma distribution rather than normal distribution. It was also observed that the out-of- control average run length performance (when process is out of control) vary greatly from normal to gamma distributions.