The Trinomial ATTRIVAR control chart

Detalhes bibliográficos
Autor(a) principal: Simoes, Felipe Domingues [UNESP]
Data de Publicação: 2020
Outros Autores: Branco Costa, Antonio Fernando, Guerreiro Machado, Marcela Aparecida [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.ijpe.2019.107559
http://hdl.handle.net/11449/196764
Resumo: In this article, we propose the Trinomial - ATTRIVAR (T-ATTRIVAR) control chart where attribute and variable sample data are used to control the process mean. Firstly, two discriminating limits sort the sample items into three excluding categories; that is, items in categories A, B, or AB, are, respectively, items with X dimensions smaller than the lower discriminating limit, larger than the upper discriminating limit, or neither smaller than the lower discriminating limit nor larger than the upper discriminating limit. Depending on the number of sample items in each category, one of three decisions is made: the process is declared in-control, the process is declared out-of-control, or all sample items are also measured. In this last case, the sample mean of X is used to decide the state of the process. Aslam et al. (2015) worked with the particular case where the sample items are classified as defective (items in category - A plus items in category - B) or not-defective (items in category - AB). The strategy of splitting defectives into two excluding categories (A and B) enhances the performance of the ATTRIVAR chart. It is worth to emphasize that the previous attribute classification truncates the X distribution. Consequently, the mathematical development to obtain the ARLs is complex - the Average Run length (ARL) is the average number of samples the control chart requires to signal. With the density function of the sum of truncated X distributions, we obtained the exact ARLs. The exact minimum ARLs are lower than the minimum ARLs Ho and Aparisi (2016) obtained with the Genetic Algorithm.
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spelling The Trinomial ATTRIVAR control chartShewhart control chartATTRIVAR control chartTruncated normal distributionsAverage run lengthMonitoring process meanIn this article, we propose the Trinomial - ATTRIVAR (T-ATTRIVAR) control chart where attribute and variable sample data are used to control the process mean. Firstly, two discriminating limits sort the sample items into three excluding categories; that is, items in categories A, B, or AB, are, respectively, items with X dimensions smaller than the lower discriminating limit, larger than the upper discriminating limit, or neither smaller than the lower discriminating limit nor larger than the upper discriminating limit. Depending on the number of sample items in each category, one of three decisions is made: the process is declared in-control, the process is declared out-of-control, or all sample items are also measured. In this last case, the sample mean of X is used to decide the state of the process. Aslam et al. (2015) worked with the particular case where the sample items are classified as defective (items in category - A plus items in category - B) or not-defective (items in category - AB). The strategy of splitting defectives into two excluding categories (A and B) enhances the performance of the ATTRIVAR chart. It is worth to emphasize that the previous attribute classification truncates the X distribution. Consequently, the mathematical development to obtain the ARLs is complex - the Average Run length (ARL) is the average number of samples the control chart requires to signal. With the density function of the sum of truncated X distributions, we obtained the exact ARLs. The exact minimum ARLs are lower than the minimum ARLs Ho and Aparisi (2016) obtained with the Genetic Algorithm.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Univ Estadual Paulista, Dept Prod, Campus Guaratingueta, Sao Paulo, SP, BrazilUniv Fed Itajuba, Itajuba, MG, BrazilUniv Estadual Paulista, Dept Prod, Campus Guaratingueta, Sao Paulo, SP, BrazilFAPESP: 2018/07147-0CNPq: 306671/2015-0CNPq: 304599/2015-8Elsevier B.V.Universidade Estadual Paulista (Unesp)Univ Fed ItajubaSimoes, Felipe Domingues [UNESP]Branco Costa, Antonio FernandoGuerreiro Machado, Marcela Aparecida [UNESP]2020-12-10T19:55:26Z2020-12-10T19:55:26Z2020-06-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article8http://dx.doi.org/10.1016/j.ijpe.2019.107559International Journal Of Production Economics. Amsterdam: Elsevier, v. 224, 8 p., 2020.0925-5273http://hdl.handle.net/11449/19676410.1016/j.ijpe.2019.107559WOS:000525321800014Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal Of Production Economicsinfo:eu-repo/semantics/openAccess2024-07-02T17:37:20Zoai:repositorio.unesp.br:11449/196764Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T22:29:43.018208Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv The Trinomial ATTRIVAR control chart
title The Trinomial ATTRIVAR control chart
spellingShingle The Trinomial ATTRIVAR control chart
Simoes, Felipe Domingues [UNESP]
Shewhart control chart
ATTRIVAR control chart
Truncated normal distributions
Average run length
Monitoring process mean
title_short The Trinomial ATTRIVAR control chart
title_full The Trinomial ATTRIVAR control chart
title_fullStr The Trinomial ATTRIVAR control chart
title_full_unstemmed The Trinomial ATTRIVAR control chart
title_sort The Trinomial ATTRIVAR control chart
author Simoes, Felipe Domingues [UNESP]
author_facet Simoes, Felipe Domingues [UNESP]
Branco Costa, Antonio Fernando
Guerreiro Machado, Marcela Aparecida [UNESP]
author_role author
author2 Branco Costa, Antonio Fernando
Guerreiro Machado, Marcela Aparecida [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Univ Fed Itajuba
dc.contributor.author.fl_str_mv Simoes, Felipe Domingues [UNESP]
Branco Costa, Antonio Fernando
Guerreiro Machado, Marcela Aparecida [UNESP]
dc.subject.por.fl_str_mv Shewhart control chart
ATTRIVAR control chart
Truncated normal distributions
Average run length
Monitoring process mean
topic Shewhart control chart
ATTRIVAR control chart
Truncated normal distributions
Average run length
Monitoring process mean
description In this article, we propose the Trinomial - ATTRIVAR (T-ATTRIVAR) control chart where attribute and variable sample data are used to control the process mean. Firstly, two discriminating limits sort the sample items into three excluding categories; that is, items in categories A, B, or AB, are, respectively, items with X dimensions smaller than the lower discriminating limit, larger than the upper discriminating limit, or neither smaller than the lower discriminating limit nor larger than the upper discriminating limit. Depending on the number of sample items in each category, one of three decisions is made: the process is declared in-control, the process is declared out-of-control, or all sample items are also measured. In this last case, the sample mean of X is used to decide the state of the process. Aslam et al. (2015) worked with the particular case where the sample items are classified as defective (items in category - A plus items in category - B) or not-defective (items in category - AB). The strategy of splitting defectives into two excluding categories (A and B) enhances the performance of the ATTRIVAR chart. It is worth to emphasize that the previous attribute classification truncates the X distribution. Consequently, the mathematical development to obtain the ARLs is complex - the Average Run length (ARL) is the average number of samples the control chart requires to signal. With the density function of the sum of truncated X distributions, we obtained the exact ARLs. The exact minimum ARLs are lower than the minimum ARLs Ho and Aparisi (2016) obtained with the Genetic Algorithm.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-10T19:55:26Z
2020-12-10T19:55:26Z
2020-06-01
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/10.1016/j.ijpe.2019.107559
International Journal Of Production Economics. Amsterdam: Elsevier, v. 224, 8 p., 2020.
0925-5273
http://hdl.handle.net/11449/196764
10.1016/j.ijpe.2019.107559
WOS:000525321800014
url http://dx.doi.org/10.1016/j.ijpe.2019.107559
http://hdl.handle.net/11449/196764
identifier_str_mv International Journal Of Production Economics. Amsterdam: Elsevier, v. 224, 8 p., 2020.
0925-5273
10.1016/j.ijpe.2019.107559
WOS:000525321800014
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv International Journal Of Production Economics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 8
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv Web of Science
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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