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A Study on the Median Run Length Performance of the Run Sum S Control Chart

Gao Han 1, Khoo Michael Boon Chong 1, Teh Sin Yin 2, and Teoh Wei Lin 3
1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Minden, Penang, Malaysia
2. School of Management, Universiti Sains Malaysia, 11800 Minden, Penang, Malaysia
3. School of Mathematical & Computer Sciences, Heriot-Watt University Malaysia, 62200 Putrajaya, Malaysia

Abstract—Control charts play a very important role in Statistical Process Control. Run sum S control chart is sensitive in detecting small to moderate shifts. It is an excellent alternative to Shewhart control chart. The performance of the run sum S control chart based on median run length (MRL) performance is proposed in this study. The Statistical Analysis System (SAS) program was used to calculate the in-control ARL and in-control MRL for the nine run sum S chart schemes with different sample sizes, magnitude of shift in the process standard deviation, and the in-control run lengths. The findings show that the MRL measure provides better explanation than the ARL criterion. Moreover, the MRL performance of the run sum S chart schemes is substantially affected by the sample sizes, magnitude of shift in the process standard deviation, and the in-control run lengths.

Index Terms—run sum S chart, average run length (ARL), median run length (MRL), process standard deviation

Cite: Gao Han, Khoo Michael Boon Chong, Teh Sin Yin, and Teoh Wei Lin, "A Study on the Median Run Length Performance of the Run Sum S Control Chart" International Journal of Mechanical Engineering and Robotics Research, Vol. 8, No. 6, pp. 885-890, November 2019. DOI: 10.18178/ijmerr.8.6.885-890