Objective Bayesian inference for the capability index of the Gamma distribution
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1002/qre.2854 http://hdl.handle.net/11449/210047 |
Resumo: | The Gamma distribution has been applied in research in several areas of knowledge, due to its good flexibility and adaptability nature. Process capacity indices like Cpk are widely used when the measurements related to the data follow a normal distribution. This article aims to estimate the Cpk index for nonnormal data using the Gamma distribution. We discuss maximum likelihood estimation and a Bayesian analysis through the Gamma distribution using an objective prior, known as a matching prior that can return Bayesian estimates with good properties for the Cpk. A comparative study is made between classical and Bayesian estimation. The proposed Bayesian approach is considered with the Markov chain Monte Carlo method to generate samples of the posterior distribution. A simulation study is carried out to verify whether the posterior distribution presents good results when compared with the classical approach in terms of the mean relative errors and the mean square errors, which are the two commonly used metrics to evaluate the parameter estimators. Based on the real dataset, Bayesian estimates and credibility intervals for unknown parameters and the prior distribution are achieved to verify if the process is under control. |
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Repositório Institucional da UNESP |
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Objective Bayesian inference for the capability index of the Gamma distribution<mmlmath altimg=urnx-wiley07488017mediaqre2854qre2854-math-0001 display=inline><mmlmsub><mmlmi>C</mmlmi><mmlmrow><mmlmi>p</mmlmi>k</mmlmi></mmlmrow></mmlmsub></mmlmath>matching priorobjective Bayesian inferenceprocess capacity indexThe Gamma distribution has been applied in research in several areas of knowledge, due to its good flexibility and adaptability nature. Process capacity indices like Cpk are widely used when the measurements related to the data follow a normal distribution. This article aims to estimate the Cpk index for nonnormal data using the Gamma distribution. We discuss maximum likelihood estimation and a Bayesian analysis through the Gamma distribution using an objective prior, known as a matching prior that can return Bayesian estimates with good properties for the Cpk. A comparative study is made between classical and Bayesian estimation. The proposed Bayesian approach is considered with the Markov chain Monte Carlo method to generate samples of the posterior distribution. A simulation study is carried out to verify whether the posterior distribution presents good results when compared with the classical approach in terms of the mean relative errors and the mean square errors, which are the two commonly used metrics to evaluate the parameter estimators. Based on the real dataset, Bayesian estimates and credibility intervals for unknown parameters and the prior distribution are achieved to verify if the process is under control.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)State Univ Sao Paulo, Dept Stat, Presidente Prudente, SP, BrazilUniv Sao Paulo, Inst Math & Comp Sci, Sao Carlos, SP, BrazilUniv Dodoma, Dept Math & Stat, Dodoma, TanzaniaState Univ Sao Paulo, Dept Stat, Presidente Prudente, SP, BrazilFAPESP: 2017/25971-0Wiley-BlackwellUniversidade Estadual Paulista (Unesp)Universidade de São Paulo (USP)Univ DodomaAlmeida, Marcello Henrique de [UNESP]Ramos, Pedro LuizRao, Gadde SrinivasaMoala, Fernando Antonio [UNESP]2021-06-25T12:38:03Z2021-06-25T12:38:03Z2021-02-17info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article13http://dx.doi.org/10.1002/qre.2854Quality And Reliability Engineering International. Hoboken: Wiley, 13 p., 2021.0748-8017http://hdl.handle.net/11449/21004710.1002/qre.2854WOS:000618764000001Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengQuality And Reliability Engineering Internationalinfo:eu-repo/semantics/openAccess2024-06-18T18:17:55Zoai:repositorio.unesp.br:11449/210047Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T15:58:11.724310Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Objective Bayesian inference for the capability index of the Gamma distribution |
title |
Objective Bayesian inference for the capability index of the Gamma distribution |
spellingShingle |
Objective Bayesian inference for the capability index of the Gamma distribution Almeida, Marcello Henrique de [UNESP] <mml math altimg=urn x-wiley 07488017 media qre2854 qre2854-math-0001 display=inline><mml msub><mml mi>C</mml mi><mml mrow><mml mi>p</mml mi>k</mml mi></mml mrow></mml msub></mml math> matching prior objective Bayesian inference process capacity index |
title_short |
Objective Bayesian inference for the capability index of the Gamma distribution |
title_full |
Objective Bayesian inference for the capability index of the Gamma distribution |
title_fullStr |
Objective Bayesian inference for the capability index of the Gamma distribution |
title_full_unstemmed |
Objective Bayesian inference for the capability index of the Gamma distribution |
title_sort |
Objective Bayesian inference for the capability index of the Gamma distribution |
author |
Almeida, Marcello Henrique de [UNESP] |
author_facet |
Almeida, Marcello Henrique de [UNESP] Ramos, Pedro Luiz Rao, Gadde Srinivasa Moala, Fernando Antonio [UNESP] |
author_role |
author |
author2 |
Ramos, Pedro Luiz Rao, Gadde Srinivasa Moala, Fernando Antonio [UNESP] |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Universidade de São Paulo (USP) Univ Dodoma |
dc.contributor.author.fl_str_mv |
Almeida, Marcello Henrique de [UNESP] Ramos, Pedro Luiz Rao, Gadde Srinivasa Moala, Fernando Antonio [UNESP] |
dc.subject.por.fl_str_mv |
<mml math altimg=urn x-wiley 07488017 media qre2854 qre2854-math-0001 display=inline><mml msub><mml mi>C</mml mi><mml mrow><mml mi>p</mml mi>k</mml mi></mml mrow></mml msub></mml math> matching prior objective Bayesian inference process capacity index |
topic |
<mml math altimg=urn x-wiley 07488017 media qre2854 qre2854-math-0001 display=inline><mml msub><mml mi>C</mml mi><mml mrow><mml mi>p</mml mi>k</mml mi></mml mrow></mml msub></mml math> matching prior objective Bayesian inference process capacity index |
description |
The Gamma distribution has been applied in research in several areas of knowledge, due to its good flexibility and adaptability nature. Process capacity indices like Cpk are widely used when the measurements related to the data follow a normal distribution. This article aims to estimate the Cpk index for nonnormal data using the Gamma distribution. We discuss maximum likelihood estimation and a Bayesian analysis through the Gamma distribution using an objective prior, known as a matching prior that can return Bayesian estimates with good properties for the Cpk. A comparative study is made between classical and Bayesian estimation. The proposed Bayesian approach is considered with the Markov chain Monte Carlo method to generate samples of the posterior distribution. A simulation study is carried out to verify whether the posterior distribution presents good results when compared with the classical approach in terms of the mean relative errors and the mean square errors, which are the two commonly used metrics to evaluate the parameter estimators. Based on the real dataset, Bayesian estimates and credibility intervals for unknown parameters and the prior distribution are achieved to verify if the process is under control. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-25T12:38:03Z 2021-06-25T12:38:03Z 2021-02-17 |
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.2854 Quality And Reliability Engineering International. Hoboken: Wiley, 13 p., 2021. 0748-8017 http://hdl.handle.net/11449/210047 10.1002/qre.2854 WOS:000618764000001 |
url |
http://dx.doi.org/10.1002/qre.2854 http://hdl.handle.net/11449/210047 |
identifier_str_mv |
Quality And Reliability Engineering International. Hoboken: Wiley, 13 p., 2021. 0748-8017 10.1002/qre.2854 WOS:000618764000001 |
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 |
13 |
dc.publisher.none.fl_str_mv |
Wiley-Blackwell |
publisher.none.fl_str_mv |
Wiley-Blackwell |
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 |
|
_version_ |
1808128587888328704 |