Q-weibull generalized renewal process with reliability applications
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/24934 |
Resumo: | Generalized Renewal Process (GRP) is a probabilistic model for repairable systems that can represent any of the five possible post-repair states of an equipment: as new condition, as old condition, as an intermediate state between new and old conditions, a better condition and a worse condition. GRP is often coupled with the Weibull distribution to model the equipment failure process and the Weibull-based GRP is able to accommodate three types of hazard rate functions: monotonically increasing, monotonically decreasing and constant. This work proposes a novel approach of GRP based on the q-Weibull distribution, which has the Weibull model as a particular case. The q-Weibull distribution has the capability of modeling two additional hazard rate behaviors, namely bathtub-shaped and unimodal curves. Such flexibility is related to a pair of parameters that govern the shape of the distribution, instead of a single parameter as in the Weibull model. In this way, the developed q-Weibull-based GRP is a more general framework that can model a variety of practical situations in the context of reliability and maintenance. The maximum likelihood problems associated with the qWeibull-based GRP using Kijima’s virtual age type I and II for the failure and time terminated cases are developed. The probabilistic and derivative-free heuristic Particle Swarm Optimization (PSO) is used to obtain the q-Weibull-based GRP paramaters’ estimates. The proposed methodology is applied to examples involving equipment failure data from literature and the obtained results indicate that the q-Weibull-based GRP may be a promising tool to model repairable systems. |
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CORRÊA, Thaís Limahttp://lattes.cnpq.br/9143311557787359http://lattes.cnpq.br/5632602851077460LINS, Isis Didier2018-06-29T19:10:32Z2018-06-29T19:10:32Z2017-02-21https://repositorio.ufpe.br/handle/123456789/24934Generalized Renewal Process (GRP) is a probabilistic model for repairable systems that can represent any of the five possible post-repair states of an equipment: as new condition, as old condition, as an intermediate state between new and old conditions, a better condition and a worse condition. GRP is often coupled with the Weibull distribution to model the equipment failure process and the Weibull-based GRP is able to accommodate three types of hazard rate functions: monotonically increasing, monotonically decreasing and constant. This work proposes a novel approach of GRP based on the q-Weibull distribution, which has the Weibull model as a particular case. The q-Weibull distribution has the capability of modeling two additional hazard rate behaviors, namely bathtub-shaped and unimodal curves. Such flexibility is related to a pair of parameters that govern the shape of the distribution, instead of a single parameter as in the Weibull model. In this way, the developed q-Weibull-based GRP is a more general framework that can model a variety of practical situations in the context of reliability and maintenance. The maximum likelihood problems associated with the qWeibull-based GRP using Kijima’s virtual age type I and II for the failure and time terminated cases are developed. The probabilistic and derivative-free heuristic Particle Swarm Optimization (PSO) is used to obtain the q-Weibull-based GRP paramaters’ estimates. The proposed methodology is applied to examples involving equipment failure data from literature and the obtained results indicate that the q-Weibull-based GRP may be a promising tool to model repairable systems.CAPESO Processo de Renovação Generalizado (PRG) pode ser definido como um modelo probabilístico de sistemas reparáveis capaz de representar os cinco possíveis estados do sistema após o reparo: condição de um equipamento novo, condição de um equipamento antigo, um estado intermediário entre novo e antigo, melhor do que novo e pior do que antigo. O PRG costuma ser comumente empregado junto com a distribuição Weibull para a modelagem do processo de falhas dos equipamentos, no entanto, o modelo de GRP baseado na distribuição Weibull é capaz de considerar três comportamentos de taxa de falha: monotonicamente crescente, monotonicamente decrescente e constante. Este trabalho propõe uma nova abordagem para o PRG baseado na distribuição q-Weibull, que apresenta como um de seus casos particulares a distribuição Weibull. A distribuição q-Weibull apresenta a capacidade de modelar dois comportamentos de falha adicionais, denominadas curva da banheira e curva unimodal. Esta flexibilidade está relacionada a dois parâmetros que definem o formato da distribuição, ao invés de um único parâmetro como no caso da Weibull. Dessa forma, o modelo de PRG baseado na q-Weibull pode ser considerado uma estrutura mais geral de modelagem de uma variedade de situações práticas no contexto da confiabilidade e manutenção. São desenvolvidos estimadores de máxima verossimilhança para os casos de PRG baseada na distribuição q-Weibull sendo utilizadas as idades virtuais Kijima tipo I e II para os casos de dados censurados e não censurados. A heurística probabilística e livre de derivadas denominada Otimização via Nuvem de Partículas (Particle Swarm Optimization - PSO) é utilizada para obter os estimadores de máxima verossimilhança do modelo. O modelo proposto é aplicado a exemplos envolvendo falhas de equipamentos retirados da literatura e os resultados obtidos indicam que o PRG baseado na q-Weibull é uma ferramenta promissora na modelagem de sistemas reparáveis.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em Engenharia de ProducaoUFPEBrasilAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessEngenharia de Produção.Generalized renewal processKijima type IKijima type IIq-WeibullBathtub curve.Q-weibull generalized renewal process with reliability applicationsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesismestradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETHUMBNAILDISSERTAÇÃO Thaís Lima Corrêa.pdf.jpgDISSERTAÇÃO Thaís Lima Corrêa.pdf.jpgGenerated Thumbnailimage/jpeg1298https://repositorio.ufpe.br/bitstream/123456789/24934/5/DISSERTA%c3%87%c3%83O%20Tha%c3%ads%20Lima%20Corr%c3%aaa.pdf.jpg380edb61f30e8ccda9df8d832307fc1cMD55ORIGINALDISSERTAÇÃO Thaís Lima Corrêa.pdfDISSERTAÇÃO Thaís Lima Corrêa.pdfapplication/pdf1826347https://repositorio.ufpe.br/bitstream/123456789/24934/1/DISSERTA%c3%87%c3%83O%20Tha%c3%ads%20Lima%20Corr%c3%aaa.pdf3e2a4eaa7d0d1c4c2e98d8d8e9bec071MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv |
Q-weibull generalized renewal process with reliability applications |
title |
Q-weibull generalized renewal process with reliability applications |
spellingShingle |
Q-weibull generalized renewal process with reliability applications CORRÊA, Thaís Lima Engenharia de Produção .Generalized renewal process Kijima type I Kijima type II q-Weibull Bathtub curve. |
title_short |
Q-weibull generalized renewal process with reliability applications |
title_full |
Q-weibull generalized renewal process with reliability applications |
title_fullStr |
Q-weibull generalized renewal process with reliability applications |
title_full_unstemmed |
Q-weibull generalized renewal process with reliability applications |
title_sort |
Q-weibull generalized renewal process with reliability applications |
author |
CORRÊA, Thaís Lima |
author_facet |
CORRÊA, Thaís Lima |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/9143311557787359 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/5632602851077460 |
dc.contributor.author.fl_str_mv |
CORRÊA, Thaís Lima |
dc.contributor.advisor1.fl_str_mv |
LINS, Isis Didier |
contributor_str_mv |
LINS, Isis Didier |
dc.subject.por.fl_str_mv |
Engenharia de Produção .Generalized renewal process Kijima type I Kijima type II q-Weibull Bathtub curve. |
topic |
Engenharia de Produção .Generalized renewal process Kijima type I Kijima type II q-Weibull Bathtub curve. |
description |
Generalized Renewal Process (GRP) is a probabilistic model for repairable systems that can represent any of the five possible post-repair states of an equipment: as new condition, as old condition, as an intermediate state between new and old conditions, a better condition and a worse condition. GRP is often coupled with the Weibull distribution to model the equipment failure process and the Weibull-based GRP is able to accommodate three types of hazard rate functions: monotonically increasing, monotonically decreasing and constant. This work proposes a novel approach of GRP based on the q-Weibull distribution, which has the Weibull model as a particular case. The q-Weibull distribution has the capability of modeling two additional hazard rate behaviors, namely bathtub-shaped and unimodal curves. Such flexibility is related to a pair of parameters that govern the shape of the distribution, instead of a single parameter as in the Weibull model. In this way, the developed q-Weibull-based GRP is a more general framework that can model a variety of practical situations in the context of reliability and maintenance. The maximum likelihood problems associated with the qWeibull-based GRP using Kijima’s virtual age type I and II for the failure and time terminated cases are developed. The probabilistic and derivative-free heuristic Particle Swarm Optimization (PSO) is used to obtain the q-Weibull-based GRP paramaters’ estimates. The proposed methodology is applied to examples involving equipment failure data from literature and the obtained results indicate that the q-Weibull-based GRP may be a promising tool to model repairable systems. |
publishDate |
2017 |
dc.date.issued.fl_str_mv |
2017-02-21 |
dc.date.accessioned.fl_str_mv |
2018-06-29T19:10:32Z |
dc.date.available.fl_str_mv |
2018-06-29T19:10:32Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/24934 |
url |
https://repositorio.ufpe.br/handle/123456789/24934 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.publisher.program.fl_str_mv |
Programa de Pos Graduacao em Engenharia de Producao |
dc.publisher.initials.fl_str_mv |
UFPE |
dc.publisher.country.fl_str_mv |
Brasil |
publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFPE instname:Universidade Federal de Pernambuco (UFPE) instacron:UFPE |
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UFPE |
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UFPE |
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Repositório Institucional da UFPE |
collection |
Repositório Institucional da UFPE |
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