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On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion

Recent researches on the control charts with unknown process parameters have noticed the large variability in the conditional in-control average run length (ARL) performance of control charts, especially when a small number of Phase I samples is used to estimate the process parameters. Some research...

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Detalles Bibliográficos
Autores principales: Hu, XueLong, Tang, AnAn, Qiao, YuLong, Sun, JinSheng, Guo, BaoCai
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7535069/
https://www.ncbi.nlm.nih.gov/pubmed/33017409
http://dx.doi.org/10.1371/journal.pone.0239538
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author Hu, XueLong
Tang, AnAn
Qiao, YuLong
Sun, JinSheng
Guo, BaoCai
author_facet Hu, XueLong
Tang, AnAn
Qiao, YuLong
Sun, JinSheng
Guo, BaoCai
author_sort Hu, XueLong
collection PubMed
description Recent researches on the control charts with unknown process parameters have noticed the large variability in the conditional in-control average run length (ARL) performance of control charts, especially when a small number of Phase I samples is used to estimate the process parameters. Some research works have been conducted on the conditional ARL performance of different types of control charts. In this paper, by simulating the empirical distribution of the conditional ARL and especially using the exceedance probability criterion (EPC), we study the conditional ARL performance of the synthetic [Image: see text] chart. Our results show that a large amount of Phase I samples is needed to obtain a specified EPC of the synthetic chart. For the available number of Phase I samples, the control limits of the synthetic chart are adjusted using the EPC method to improve its conditional in-control performance. It is shown that, for small mean shift sizes, a tradeoff should be made between the conditional in-control and out-of-control performances. For moderate to large shifts, the conditional performance of the synthetic chart using the adjusted control limits is generally satisfied. By comparing the results with the ones using the bootstrap approach, it can also be concluded that the conditional performances of both approaches are comparable. While the method proposed in this paper requires much less computation work than the bootstrap approach.
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spelling pubmed-75350692020-10-15 On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion Hu, XueLong Tang, AnAn Qiao, YuLong Sun, JinSheng Guo, BaoCai PLoS One Research Article Recent researches on the control charts with unknown process parameters have noticed the large variability in the conditional in-control average run length (ARL) performance of control charts, especially when a small number of Phase I samples is used to estimate the process parameters. Some research works have been conducted on the conditional ARL performance of different types of control charts. In this paper, by simulating the empirical distribution of the conditional ARL and especially using the exceedance probability criterion (EPC), we study the conditional ARL performance of the synthetic [Image: see text] chart. Our results show that a large amount of Phase I samples is needed to obtain a specified EPC of the synthetic chart. For the available number of Phase I samples, the control limits of the synthetic chart are adjusted using the EPC method to improve its conditional in-control performance. It is shown that, for small mean shift sizes, a tradeoff should be made between the conditional in-control and out-of-control performances. For moderate to large shifts, the conditional performance of the synthetic chart using the adjusted control limits is generally satisfied. By comparing the results with the ones using the bootstrap approach, it can also be concluded that the conditional performances of both approaches are comparable. While the method proposed in this paper requires much less computation work than the bootstrap approach. Public Library of Science 2020-10-05 /pmc/articles/PMC7535069/ /pubmed/33017409 http://dx.doi.org/10.1371/journal.pone.0239538 Text en © 2020 Hu et al http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Hu, XueLong
Tang, AnAn
Qiao, YuLong
Sun, JinSheng
Guo, BaoCai
On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion
title On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion
title_full On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion
title_fullStr On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion
title_full_unstemmed On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion
title_short On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion
title_sort on the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7535069/
https://www.ncbi.nlm.nih.gov/pubmed/33017409
http://dx.doi.org/10.1371/journal.pone.0239538
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