Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length.

The side sensitive synthetic chart was proposed to improve the performance of the synthetic chart to monitor shifts in the coefficient of variation (γ), by incorporating the side sensitivity feature where successive non-conforming samples must fall on the same side of the control limits. The existin...

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Autores principales:	Waie Chung Yeong, Ping Yin Lee, Sok Li Lim, Peh Sang Ng, Khai Wah Khaw
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/3307219755bc44c694a1a1f48e59a3d9
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spelling	oai:doaj.org-article:3307219755bc44c694a1a1f48e59a3d92021-12-02T20:08:48ZOptimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length.1932-620310.1371/journal.pone.0255366https://doaj.org/article/3307219755bc44c694a1a1f48e59a3d92021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0255366https://doaj.org/toc/1932-6203The side sensitive synthetic chart was proposed to improve the performance of the synthetic chart to monitor shifts in the coefficient of variation (γ), by incorporating the side sensitivity feature where successive non-conforming samples must fall on the same side of the control limits. The existing side sensitive synthetic- γ chart is only evaluated in terms of the average run length (ARL) and expected average run length (EARL). However, the run length distribution is skewed to the right, hence the actual performance of the chart may be frequently different from what is shown by the ARL and EARL. This paper evaluates the entire run length distribution by studying the percentiles of the run length distribution. It is shown that false alarms frequently happen much earlier than the in-control ARL (ARL0), and small shifts are often detected earlier compared to the ARL1. Subsequently, this paper proposes an alternative design based on the median run length (MRL) and expected median run length (EMRL). The optimal design based on the MRL shows smaller out-of-control MRL (MRL1), which shows a quicker detection of the out-of-control condition, compared to the existing design, while the results from the optimal design based on the EMRL is similar to that of the existing designs. Comparisons with the synthetic-γ chart without side sensitivity shows that side sensitivity reduces the median number of samples required to detect a shift and reduces the variability in the run length. Finally, the proposed designs are implemented on an actual industrial example.Waie Chung YeongPing Yin LeeSok Li LimPeh Sang NgKhai Wah KhawPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 7, p e0255366 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Waie Chung Yeong Ping Yin Lee Sok Li Lim Peh Sang Ng Khai Wah Khaw Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length.
description	The side sensitive synthetic chart was proposed to improve the performance of the synthetic chart to monitor shifts in the coefficient of variation (γ), by incorporating the side sensitivity feature where successive non-conforming samples must fall on the same side of the control limits. The existing side sensitive synthetic- γ chart is only evaluated in terms of the average run length (ARL) and expected average run length (EARL). However, the run length distribution is skewed to the right, hence the actual performance of the chart may be frequently different from what is shown by the ARL and EARL. This paper evaluates the entire run length distribution by studying the percentiles of the run length distribution. It is shown that false alarms frequently happen much earlier than the in-control ARL (ARL0), and small shifts are often detected earlier compared to the ARL1. Subsequently, this paper proposes an alternative design based on the median run length (MRL) and expected median run length (EMRL). The optimal design based on the MRL shows smaller out-of-control MRL (MRL1), which shows a quicker detection of the out-of-control condition, compared to the existing design, while the results from the optimal design based on the EMRL is similar to that of the existing designs. Comparisons with the synthetic-γ chart without side sensitivity shows that side sensitivity reduces the median number of samples required to detect a shift and reduces the variability in the run length. Finally, the proposed designs are implemented on an actual industrial example.
format	article
author	Waie Chung Yeong Ping Yin Lee Sok Li Lim Peh Sang Ng Khai Wah Khaw
author_facet	Waie Chung Yeong Ping Yin Lee Sok Li Lim Peh Sang Ng Khai Wah Khaw
author_sort	Waie Chung Yeong
title	Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length.
title_short	Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length.
title_full	Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length.
title_fullStr	Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length.
title_full_unstemmed	Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length.
title_sort	optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/3307219755bc44c694a1a1f48e59a3d9
work_keys_str_mv	AT waiechungyeong optimaldesignsofthesidesensitivesyntheticchartforthecoefficientofvariationbasedonthemedianrunlengthandexpectedmedianrunlength AT pingyinlee optimaldesignsofthesidesensitivesyntheticchartforthecoefficientofvariationbasedonthemedianrunlengthandexpectedmedianrunlength AT soklilim optimaldesignsofthesidesensitivesyntheticchartforthecoefficientofvariationbasedonthemedianrunlengthandexpectedmedianrunlength AT pehsangng optimaldesignsofthesidesensitivesyntheticchartforthecoefficientofvariationbasedonthemedianrunlengthandexpectedmedianrunlength AT khaiwahkhaw optimaldesignsofthesidesensitivesyntheticchartforthecoefficientofvariationbasedonthemedianrunlengthandexpectedmedianrunlength
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Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length.

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