Monitoring the mean vector and the covariance ­matrix of multivariate processes with sample means and sample ranges

Detalhes bibliográficos
Autor(a) principal: Costa,Antônio Fernando Branco
Data de Publicação: 2011
Outros Autores: Machado,Marcela Aparecida Guerreiro
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Production
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-65132011000200003
Resumo: The joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and R charts and the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and S² charts are the most common charts used for monitoring the process mean and dispersion. With the usual sample sizes of 4 and 5, the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and R charts are slightly inferior to the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and S² charts in terms of efficiency in detecting process shifts. In this article, we show that for the multivariate case, the charts based on the standardized sample means and sample ranges (MRMAX chart) or on the standardized sample means and sample variances (MVMAX chart) are similar in terms of efficiency in detecting shifts in the mean vector and/or in the covariance matrix. User's familiarity with the computation of sample ranges is a point in favor of the MRMAX chart. An example is presented to illustrate the application of the proposed chart.
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spelling Monitoring the mean vector and the covariance ­matrix of multivariate processes with sample means and sample rangesControl chartsMean vectorCovariance matrixMultivariate processesThe joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and R charts and the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and S² charts are the most common charts used for monitoring the process mean and dispersion. With the usual sample sizes of 4 and 5, the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and R charts are slightly inferior to the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and S² charts in terms of efficiency in detecting process shifts. In this article, we show that for the multivariate case, the charts based on the standardized sample means and sample ranges (MRMAX chart) or on the standardized sample means and sample variances (MVMAX chart) are similar in terms of efficiency in detecting shifts in the mean vector and/or in the covariance matrix. User's familiarity with the computation of sample ranges is a point in favor of the MRMAX chart. An example is presented to illustrate the application of the proposed chart.Associação Brasileira de Engenharia de Produção2011-06-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-65132011000200003Production v.21 n.2 2011reponame:Productioninstname:Associação Brasileira de Engenharia de Produção (ABEPRO)instacron:ABEPRO10.1590/S0103-65132011005000029info:eu-repo/semantics/openAccessCosta,Antônio Fernando BrancoMachado,Marcela Aparecida Guerreiroeng2011-07-01T00:00:00Zoai:scielo:S0103-65132011000200003Revistahttps://www.scielo.br/j/prod/https://old.scielo.br/oai/scielo-oai.php||production@editoracubo.com.br1980-54110103-6513opendoar:2011-07-01T00:00Production - Associação Brasileira de Engenharia de Produção (ABEPRO)false
dc.title.none.fl_str_mv Monitoring the mean vector and the covariance ­matrix of multivariate processes with sample means and sample ranges
title Monitoring the mean vector and the covariance ­matrix of multivariate processes with sample means and sample ranges
spellingShingle Monitoring the mean vector and the covariance ­matrix of multivariate processes with sample means and sample ranges
Costa,Antônio Fernando Branco
Control charts
Mean vector
Covariance matrix
Multivariate processes
title_short Monitoring the mean vector and the covariance ­matrix of multivariate processes with sample means and sample ranges
title_full Monitoring the mean vector and the covariance ­matrix of multivariate processes with sample means and sample ranges
title_fullStr Monitoring the mean vector and the covariance ­matrix of multivariate processes with sample means and sample ranges
title_full_unstemmed Monitoring the mean vector and the covariance ­matrix of multivariate processes with sample means and sample ranges
title_sort Monitoring the mean vector and the covariance ­matrix of multivariate processes with sample means and sample ranges
author Costa,Antônio Fernando Branco
author_facet Costa,Antônio Fernando Branco
Machado,Marcela Aparecida Guerreiro
author_role author
author2 Machado,Marcela Aparecida Guerreiro
author2_role author
dc.contributor.author.fl_str_mv Costa,Antônio Fernando Branco
Machado,Marcela Aparecida Guerreiro
dc.subject.por.fl_str_mv Control charts
Mean vector
Covariance matrix
Multivariate processes
topic Control charts
Mean vector
Covariance matrix
Multivariate processes
description The joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and R charts and the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and S² charts are the most common charts used for monitoring the process mean and dispersion. With the usual sample sizes of 4 and 5, the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and R charts are slightly inferior to the joint <img src="/img/revistas/prod/2011nahead/aop_t6_0002_0329.jpg" /> and S² charts in terms of efficiency in detecting process shifts. In this article, we show that for the multivariate case, the charts based on the standardized sample means and sample ranges (MRMAX chart) or on the standardized sample means and sample variances (MVMAX chart) are similar in terms of efficiency in detecting shifts in the mean vector and/or in the covariance matrix. User's familiarity with the computation of sample ranges is a point in favor of the MRMAX chart. An example is presented to illustrate the application of the proposed chart.
publishDate 2011
dc.date.none.fl_str_mv 2011-06-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-65132011000200003
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-65132011000200003
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0103-65132011005000029
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Associação Brasileira de Engenharia de Produção
publisher.none.fl_str_mv Associação Brasileira de Engenharia de Produção
dc.source.none.fl_str_mv Production v.21 n.2 2011
reponame:Production
instname:Associação Brasileira de Engenharia de Produção (ABEPRO)
instacron:ABEPRO
instname_str Associação Brasileira de Engenharia de Produção (ABEPRO)
instacron_str ABEPRO
institution ABEPRO
reponame_str Production
collection Production
repository.name.fl_str_mv Production - Associação Brasileira de Engenharia de Produção (ABEPRO)
repository.mail.fl_str_mv ||production@editoracubo.com.br
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