The Revised m-of-k Runs Rule Based on Median Run Length

Runs rules are used to increase the sensitivity of the Shewhart X control chart in detecting small and moderate process mean shifts. Most of the X charts incorporating runs rules are designed based on the average run length (ARL). It is known that the shape of the run length distribution changes according to the magnitude of the shift in the process mean, ranging from highly skewed when the process is in-control to approximately symmetric when the shift is large. Since the shape of the run length distribution changes with the magnitude of the shift in the mean, the median run length (MRL) provides a more meaningful explanation about the in-control and out-of-control performances of a control chart. In this article, we propose the design of the revised m-of-k runs rule based on MRL. In addition, the standard deviation of the run length (SDRL) of the revised m-of-k rule will also be studied. The revised m-of-k runs rule, suggested by Antzoulakos and Rakitzis (2008), was originally designed based on ARL. The Markov chain technique is employed to obtain the MRLs. Compared with the standard X chart, the MRL results show that the revised rules give better performances for small and moderate mean shifts, while maintaining the same sensitivity towards large mean shifts. The MRL results are in accordance with the results obtained by Antzoulakos and Rakitzis (2008), where the rules are designed based on ARL

A modified side-sensitive synthetic chart to monitor the process mean

Please read abstract in the article.Part of this work was supported by the SARCHI Chair at the University of Pretoria. Sandile Shongwe‟s research was supported in part by the National Research Foundation and Department of Science and Technology‟s Innovation Doctoral scholarship (SFH14081591713) and Marien Graham‟s research was supported in part by the National Research Foundation (Thuthuka programme: TTK20100724000013247, Grant number: 76219).2018-01-31hb2016Statistic