Average Run Length Performance of Shewhart Control Chart with Interpretation Rules using Markov Chain Approach

Abstract

The advantage of a Shewhart X macr control chart is its simplicity and its ability to detect large process average shifts quickly. However, the Shewhart chart, which signals an out-of-control condition when a single point falls beyond a 3-sigma limit, is also known for its insensitivity to small process average shifts. In order to make the Shewhart X macr macr control chart more sensitive for small process average shifts, an additional interpretation rules has been suggested by the practitioners. Therefore, in this paper the average run length (ARL) performance of Shewhart X macr control chart with most interpretation rules used in practice was evaluated using MARKOV chain for normal and gamma distributions through by MATLAB. The results show that the in-control average run length performance (when process is in control) be fairly high for particular rule 3 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.