Run-length distribution for Shewhart control charts with runs rules†
Hyangseok Lee1 · Yongku Kim2 · Kilho Cho3
12Department of Statistics, Kyungpook National University
Correspondence to: † This paper is based on part of Hyangseok Lee’s Master Thesis.
1 Graduate Student, Department of Statistics, Kyungpook National University, Daegu 41566, Korea
2 Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea.
3 Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea. E-mail: khcho@knu.ac.kr
1 Graduate Student, Department of Statistics, Kyungpook National University, Daegu 41566, Korea
2 Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea.
3 Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea. E-mail: khcho@knu.ac.kr
Received November 26, 2022; Revised December 7, 2022; Accepted December 7, 2022.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Abstract
- The Shewhart control chart is simple to apply to the actual production process. When the change is large, it is sensitive to detect the changes. However, if the change is small, it is not sensitive. Several methods have been developed to improve the sensitivity of the Shewhart control chart. Western Electronic Company applied runs rules to have sensitivity in cases of small shifts. To calculate the ARL of the control chart, we use the finite Markov chain imbedding method of Fu and Koutras and calculate ARLs in cases of several mean and variance shifts. In this thesis, according to the small shifts in mean and variance, the two control charts were compared through ARL. The control chart with runs rules has been more decreased ARL in small shifts compared the traditional Shewhart control charts. That is, it can be seen that the control chart with runs rules detects more sensitively than the Shewhart control chart when there are small shifts.
- Keywords : Average run-length, Markov chain, run-length, runs rules, Shewhart control chart.
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