Performance comparison of the exact run-length distribution between the run sum X and EWMA X charts
The run sum (RS) X and exponentially weighted moving average (EWMA) X charts are very effective in detecting small and moderate process mean shifts. The design of the RS X and EWMA X charts based on the average run length (ARL) alone, can be misleading and confusing. This is due to the fact that...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia
2016
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| Online Access: | http://journalarticle.ukm.my/10200/ http://journalarticle.ukm.my/10200/1/jqma-12-1_2-paper2.pdf |
| _version_ | 1848812312275714048 |
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| author | Chong, J.K. Teoh, W.L. Khoo, Michael B.C. Chong, Z.L. Teh, S.Y. |
| author_facet | Chong, J.K. Teoh, W.L. Khoo, Michael B.C. Chong, Z.L. Teh, S.Y. |
| author_sort | Chong, J.K. |
| building | UKM Institutional Repository |
| collection | Online Access |
| description | The run sum (RS) X and exponentially weighted moving average (EWMA) X charts are very
effective in detecting small and moderate process mean shifts. The design of the RS X and
EWMA X charts based on the average run length (ARL) alone, can be misleading and
confusing. This is due to the fact that the run-length distribution of a control chart is highly
right-skewed when the process is in-control or slightly out-of-control; while that for the out-ofcontrol
cases, the run-length distribution is almost symmetric. On the other hand, the percentiles
of the run-length distribution provide the probability of getting a signal by a certain number of
samples. This will benefit practitioners as the percentiles of the run-length distribution give
comprehensive information regarding the behaviour of a control chart. Accordingly, this paper
provides a thorough study of the run-length properties (ARL, standard deviation of the run
length and percentiles of the run-length distribution) for the RS X and EWMA X charts.
Comparative studies show that the EWMA X chart outperforms the RS X charts for detecting
small mean shifts when all the control charts are optimized with respect to a small shift size.
However, the RS X charts surpass the EWMA X chart for all sizes of mean shifts when all
the control charts are optimized with respect to a large shift size. |
| first_indexed | 2025-11-15T00:00:18Z |
| format | Article |
| id | oai:generic.eprints.org:10200 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T00:00:18Z |
| publishDate | 2016 |
| publisher | Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org:102002017-03-15T07:08:07Z http://journalarticle.ukm.my/10200/ Performance comparison of the exact run-length distribution between the run sum X and EWMA X charts Chong, J.K. Teoh, W.L. Khoo, Michael B.C. Chong, Z.L. Teh, S.Y. The run sum (RS) X and exponentially weighted moving average (EWMA) X charts are very effective in detecting small and moderate process mean shifts. The design of the RS X and EWMA X charts based on the average run length (ARL) alone, can be misleading and confusing. This is due to the fact that the run-length distribution of a control chart is highly right-skewed when the process is in-control or slightly out-of-control; while that for the out-ofcontrol cases, the run-length distribution is almost symmetric. On the other hand, the percentiles of the run-length distribution provide the probability of getting a signal by a certain number of samples. This will benefit practitioners as the percentiles of the run-length distribution give comprehensive information regarding the behaviour of a control chart. Accordingly, this paper provides a thorough study of the run-length properties (ARL, standard deviation of the run length and percentiles of the run-length distribution) for the RS X and EWMA X charts. Comparative studies show that the EWMA X chart outperforms the RS X charts for detecting small mean shifts when all the control charts are optimized with respect to a small shift size. However, the RS X charts surpass the EWMA X chart for all sizes of mean shifts when all the control charts are optimized with respect to a large shift size. Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia 2016-12 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/10200/1/jqma-12-1_2-paper2.pdf Chong, J.K. and Teoh, W.L. and Khoo, Michael B.C. and Chong, Z.L. and Teh, S.Y. (2016) Performance comparison of the exact run-length distribution between the run sum X and EWMA X charts. Journal of Quality Measurement and Analysis, 12 (1-2). pp. 11-26. ISSN 1823-5670 http://www.ukm.my/jqma/jqma12_1_2a.html |
| spellingShingle | Chong, J.K. Teoh, W.L. Khoo, Michael B.C. Chong, Z.L. Teh, S.Y. Performance comparison of the exact run-length distribution between the run sum X and EWMA X charts |
| title | Performance comparison of the exact run-length
distribution between the run sum X and EWMA X charts |
| title_full | Performance comparison of the exact run-length
distribution between the run sum X and EWMA X charts |
| title_fullStr | Performance comparison of the exact run-length
distribution between the run sum X and EWMA X charts |
| title_full_unstemmed | Performance comparison of the exact run-length
distribution between the run sum X and EWMA X charts |
| title_short | Performance comparison of the exact run-length
distribution between the run sum X and EWMA X charts |
| title_sort | performance comparison of the exact run-length
distribution between the run sum x and ewma x charts |
| url | http://journalarticle.ukm.my/10200/ http://journalarticle.ukm.my/10200/ http://journalarticle.ukm.my/10200/1/jqma-12-1_2-paper2.pdf |