The use of principal components and univariate charts to control multivariate processes

Detalhes bibliográficos
Autor(a) principal: Machado, Marcela A. G. [UNESP]
Data de Publicação: 2008
Outros Autores: Costa, Antonio F. B. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1590/S0101-74382008000100010
http://hdl.handle.net/11449/70249
Resumo: In this article, we evaluate the performance of the T2 chart based on the principal components (PC chart) and the simultaneous univariate control charts based on the original variables (SU X̄ charts) or based on the principal components (SUPC charts). The main reason to consider the PC chart lies on the dimensionality reduction. However, depending on the disturbance and on the way the original variables are related, the chart is very slow in signaling, except when all variables are negatively correlated and the principal component is wisely selected. Comparing the SU X̄, the SUPC and the T 2 charts we conclude that the SU X̄ charts (SUPC charts) have a better overall performance when the variables are positively (negatively) correlated. We also develop the expression to obtain the power of two S 2 charts designed for monitoring the covariance matrix. These joint S2 charts are, in the majority of the cases, more efficient than the generalized variance |S| chart.
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spelling The use of principal components and univariate charts to control multivariate processesMultivariate process controlPrincipal componentSimultaneous univariate control chartsIn this article, we evaluate the performance of the T2 chart based on the principal components (PC chart) and the simultaneous univariate control charts based on the original variables (SU X̄ charts) or based on the principal components (SUPC charts). The main reason to consider the PC chart lies on the dimensionality reduction. However, depending on the disturbance and on the way the original variables are related, the chart is very slow in signaling, except when all variables are negatively correlated and the principal component is wisely selected. Comparing the SU X̄, the SUPC and the T 2 charts we conclude that the SU X̄ charts (SUPC charts) have a better overall performance when the variables are positively (negatively) correlated. We also develop the expression to obtain the power of two S 2 charts designed for monitoring the covariance matrix. These joint S2 charts are, in the majority of the cases, more efficient than the generalized variance |S| chart.Production Department São Paulo State University (UNESP), Guaratinguetá - SPProduction Department São Paulo State University (UNESP), Guaratinguetá - SPUniversidade Estadual Paulista (Unesp)Machado, Marcela A. G. [UNESP]Costa, Antonio F. B. [UNESP]2014-05-27T11:22:46Z2014-05-27T11:22:46Z2008-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article173-196application/pdfhttp://dx.doi.org/10.1590/S0101-74382008000100010Pesquisa Operacional, v. 28, n. 1, p. 173-196, 2008.0101-74381678-5142http://hdl.handle.net/11449/7024910.1590/S0101-74382008000100010S0101-743820080001000102-s2.0-467491305872-s2.0-46749130587.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPesquisa Operacional0,365info:eu-repo/semantics/openAccess2024-01-11T06:32:57Zoai:repositorio.unesp.br:11449/70249Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-01-11T06:32:57Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv The use of principal components and univariate charts to control multivariate processes
title The use of principal components and univariate charts to control multivariate processes
spellingShingle The use of principal components and univariate charts to control multivariate processes
Machado, Marcela A. G. [UNESP]
Multivariate process control
Principal component
Simultaneous univariate control charts
title_short The use of principal components and univariate charts to control multivariate processes
title_full The use of principal components and univariate charts to control multivariate processes
title_fullStr The use of principal components and univariate charts to control multivariate processes
title_full_unstemmed The use of principal components and univariate charts to control multivariate processes
title_sort The use of principal components and univariate charts to control multivariate processes
author Machado, Marcela A. G. [UNESP]
author_facet Machado, Marcela A. G. [UNESP]
Costa, Antonio F. B. [UNESP]
author_role author
author2 Costa, Antonio F. B. [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Machado, Marcela A. G. [UNESP]
Costa, Antonio F. B. [UNESP]
dc.subject.por.fl_str_mv Multivariate process control
Principal component
Simultaneous univariate control charts
topic Multivariate process control
Principal component
Simultaneous univariate control charts
description In this article, we evaluate the performance of the T2 chart based on the principal components (PC chart) and the simultaneous univariate control charts based on the original variables (SU X̄ charts) or based on the principal components (SUPC charts). The main reason to consider the PC chart lies on the dimensionality reduction. However, depending on the disturbance and on the way the original variables are related, the chart is very slow in signaling, except when all variables are negatively correlated and the principal component is wisely selected. Comparing the SU X̄, the SUPC and the T 2 charts we conclude that the SU X̄ charts (SUPC charts) have a better overall performance when the variables are positively (negatively) correlated. We also develop the expression to obtain the power of two S 2 charts designed for monitoring the covariance matrix. These joint S2 charts are, in the majority of the cases, more efficient than the generalized variance |S| chart.
publishDate 2008
dc.date.none.fl_str_mv 2008-01-01
2014-05-27T11:22:46Z
2014-05-27T11:22:46Z
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/10.1590/S0101-74382008000100010
Pesquisa Operacional, v. 28, n. 1, p. 173-196, 2008.
0101-7438
1678-5142
http://hdl.handle.net/11449/70249
10.1590/S0101-74382008000100010
S0101-74382008000100010
2-s2.0-46749130587
2-s2.0-46749130587.pdf
url http://dx.doi.org/10.1590/S0101-74382008000100010
http://hdl.handle.net/11449/70249
identifier_str_mv Pesquisa Operacional, v. 28, n. 1, p. 173-196, 2008.
0101-7438
1678-5142
10.1590/S0101-74382008000100010
S0101-74382008000100010
2-s2.0-46749130587
2-s2.0-46749130587.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Pesquisa Operacional
0,365
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 173-196
application/pdf
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
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