Monitoring bivariate and trivariate mean vectors with a Shewhart chart
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1002/qre.2165 http://hdl.handle.net/11449/228329 |
Resumo: | In this article, we propose the use of the mean chart to control multivariate processes. The basic idea is to control the mean vector of bivariate (X, Y) and trivariate (X, Y, Z) processes by alternating the charting statistic of the Shewhart chart. If the mean of X observations was the charting statistic to obtain the current sample point, then the mean of Y observations will be the charting statistic to obtain the next sample point (for the trivariate case, the mean of Z observations will be the charting statistic to obtain the sample point subsequent to the next one). As a Shewhart chart, the signal is given anytime a sample point is plotted beyond the control limits, independent of the charting statistic in use. A fair comparison between the proposed chart and the Hotelling chart is based on an equal number of measurements per sample. The Shewhart chart with alternated charting statistic (ACS) always outperforms the Hotelling chart, except for specific types of disturbances in quality characteristics highly correlated (ρ = 0.7). The ACS chart is substantially easier to operate and faster than the Hotelling chart in signaling changes in the mean vector of bivariate and trivariate processes. Even with fewer measurements per sample, the trivariate ACS chart outperforms the Hotelling chart. |
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Monitoring bivariate and trivariate mean vectors with a Shewhart chartalternating charting statisticbivariate processesShewhart charttrivariate processesIn this article, we propose the use of the mean chart to control multivariate processes. The basic idea is to control the mean vector of bivariate (X, Y) and trivariate (X, Y, Z) processes by alternating the charting statistic of the Shewhart chart. If the mean of X observations was the charting statistic to obtain the current sample point, then the mean of Y observations will be the charting statistic to obtain the next sample point (for the trivariate case, the mean of Z observations will be the charting statistic to obtain the sample point subsequent to the next one). As a Shewhart chart, the signal is given anytime a sample point is plotted beyond the control limits, independent of the charting statistic in use. A fair comparison between the proposed chart and the Hotelling chart is based on an equal number of measurements per sample. The Shewhart chart with alternated charting statistic (ACS) always outperforms the Hotelling chart, except for specific types of disturbances in quality characteristics highly correlated (ρ = 0.7). The ACS chart is substantially easier to operate and faster than the Hotelling chart in signaling changes in the mean vector of bivariate and trivariate processes. Even with fewer measurements per sample, the trivariate ACS chart outperforms the Hotelling chart.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Ensino Academia Militar de Agulhas NegrasProduction Universidade Estadual Paulista Faculdade de Engenharia de GuaratinguetéProduction Universidade Estadual Paulista Faculdade de Engenharia de GuaratinguetéCNPq: 304599/2015-8CNPq: 402559/2016-9Academia Militar de Agulhas NegrasUniversidade Estadual Paulista (UNESP)Leoni, Roberto CamposCosta, Antonio Fernando Branco [UNESP]2022-04-29T08:03:59Z2022-04-29T08:03:59Z2017-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article2035-2042http://dx.doi.org/10.1002/qre.2165Quality and Reliability Engineering International, v. 33, n. 8, p. 2035-2042, 2017.1099-16380748-8017http://hdl.handle.net/11449/22832910.1002/qre.21652-s2.0-85019741123Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengQuality and Reliability Engineering Internationalinfo:eu-repo/semantics/openAccess2024-07-02T17:37:20Zoai:repositorio.unesp.br:11449/228329Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:22:43.445772Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Monitoring bivariate and trivariate mean vectors with a Shewhart chart |
title |
Monitoring bivariate and trivariate mean vectors with a Shewhart chart |
spellingShingle |
Monitoring bivariate and trivariate mean vectors with a Shewhart chart Leoni, Roberto Campos alternating charting statistic bivariate processes Shewhart chart trivariate processes |
title_short |
Monitoring bivariate and trivariate mean vectors with a Shewhart chart |
title_full |
Monitoring bivariate and trivariate mean vectors with a Shewhart chart |
title_fullStr |
Monitoring bivariate and trivariate mean vectors with a Shewhart chart |
title_full_unstemmed |
Monitoring bivariate and trivariate mean vectors with a Shewhart chart |
title_sort |
Monitoring bivariate and trivariate mean vectors with a Shewhart chart |
author |
Leoni, Roberto Campos |
author_facet |
Leoni, Roberto Campos Costa, Antonio Fernando Branco [UNESP] |
author_role |
author |
author2 |
Costa, Antonio Fernando Branco [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Academia Militar de Agulhas Negras Universidade Estadual Paulista (UNESP) |
dc.contributor.author.fl_str_mv |
Leoni, Roberto Campos Costa, Antonio Fernando Branco [UNESP] |
dc.subject.por.fl_str_mv |
alternating charting statistic bivariate processes Shewhart chart trivariate processes |
topic |
alternating charting statistic bivariate processes Shewhart chart trivariate processes |
description |
In this article, we propose the use of the mean chart to control multivariate processes. The basic idea is to control the mean vector of bivariate (X, Y) and trivariate (X, Y, Z) processes by alternating the charting statistic of the Shewhart chart. If the mean of X observations was the charting statistic to obtain the current sample point, then the mean of Y observations will be the charting statistic to obtain the next sample point (for the trivariate case, the mean of Z observations will be the charting statistic to obtain the sample point subsequent to the next one). As a Shewhart chart, the signal is given anytime a sample point is plotted beyond the control limits, independent of the charting statistic in use. A fair comparison between the proposed chart and the Hotelling chart is based on an equal number of measurements per sample. The Shewhart chart with alternated charting statistic (ACS) always outperforms the Hotelling chart, except for specific types of disturbances in quality characteristics highly correlated (ρ = 0.7). The ACS chart is substantially easier to operate and faster than the Hotelling chart in signaling changes in the mean vector of bivariate and trivariate processes. Even with fewer measurements per sample, the trivariate ACS chart outperforms the Hotelling chart. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-12-01 2022-04-29T08:03:59Z 2022-04-29T08:03:59Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1002/qre.2165 Quality and Reliability Engineering International, v. 33, n. 8, p. 2035-2042, 2017. 1099-1638 0748-8017 http://hdl.handle.net/11449/228329 10.1002/qre.2165 2-s2.0-85019741123 |
url |
http://dx.doi.org/10.1002/qre.2165 http://hdl.handle.net/11449/228329 |
identifier_str_mv |
Quality and Reliability Engineering International, v. 33, n. 8, p. 2035-2042, 2017. 1099-1638 0748-8017 10.1002/qre.2165 2-s2.0-85019741123 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Quality and Reliability Engineering International |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
2035-2042 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129514131161088 |