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 change...
| Автори: | , , , |
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| Інші автори: | |
| Формат: | Journal Article |
| Мова: | English |
| Опубліковано: |
2013
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| Онлайн доступ: | https://hdl.handle.net/10356/85389 http://hdl.handle.net/10220/13057 |
| _version_ | 1826121019566325760 |
|---|---|
| author | Low, Chun Kit. Khoo, Michael B. C. Teoh, Wei Lin. Wu, Zhang. |
| author2 | School of Mechanical and Aerospace Engineering |
| author_facet | School of Mechanical and Aerospace Engineering Low, Chun Kit. Khoo, Michael B. C. Teoh, Wei Lin. Wu, Zhang. |
| author_sort | Low, Chun Kit. |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T05:25:54Z |
| format | Journal Article |
| id | ntu-10356/85389 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:25:54Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/853892020-03-07T13:19:23Z The revised m-of-k runs rule based on median run length Low, Chun Kit. Khoo, Michael B. C. Teoh, Wei Lin. Wu, Zhang. School of Mechanical and Aerospace Engineering 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. 2013-08-06T06:06:05Z 2019-12-06T16:02:53Z 2013-08-06T06:06:05Z 2019-12-06T16:02:53Z 2012 2012 Journal Article Low, C. K., Khoo, M. B. C., Teoh, W. L.,& Wu, Z. (2012). The Revised m-of-k Runs Rule Based on Median Run Length. Communications in Statistics - Simulation and Computation, 41(8), 1463-1477. https://hdl.handle.net/10356/85389 http://hdl.handle.net/10220/13057 10.1080/03610918.2011.606950 en Communications in statistics - simulation and computation |
| spellingShingle | Low, Chun Kit. Khoo, Michael B. C. Teoh, Wei Lin. Wu, Zhang. The revised m-of-k runs rule based on median run length |
| title | The revised m-of-k runs rule based on median run length |
| title_full | The revised m-of-k runs rule based on median run length |
| title_fullStr | The revised m-of-k runs rule based on median run length |
| title_full_unstemmed | The revised m-of-k runs rule based on median run length |
| title_short | The revised m-of-k runs rule based on median run length |
| title_sort | revised m of k runs rule based on median run length |
| url | https://hdl.handle.net/10356/85389 http://hdl.handle.net/10220/13057 |
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