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...

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Main Authors:	Chong, J.K., Teoh, W.L., Khoo, Michael B.C., Chong, Z.L., Teh, S.Y.
Format:	Article
Language:	English
Published:	Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia 2016
Online Access:	http://journalarticle.ukm.my/10200/ http://journalarticle.ukm.my/10200/ http://journalarticle.ukm.my/10200/1/jqma-12-1_2-paper2.pdf

id	ukm-10200
recordtype	eprints
spelling	ukm-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
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
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.
format	Article
author	Chong, J.K. Teoh, W.L. Khoo, Michael B.C. Chong, Z.L. Teh, S.Y.
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
author_facet	Chong, J.K. Teoh, W.L. Khoo, Michael B.C. Chong, Z.L. Teh, S.Y.
author_sort	Chong, J.K.
title	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_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_sort	performance comparison of the exact run-length distribution between the run sum x and ewma x charts
publisher	Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia
publishDate	2016
url	http://journalarticle.ukm.my/10200/ http://journalarticle.ukm.my/10200/ http://journalarticle.ukm.my/10200/1/jqma-12-1_2-paper2.pdf
first_indexed	2023-09-18T19:56:46Z
last_indexed	2023-09-18T19:56:46Z
_version_	1777406581902671872

Performance comparison of the exact run-length distribution between the run sum X and EWMA X charts

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