Reliability analysis of repairable systems considering unobserved heterogeneity and competing risks
Autor(a) principal: | |
---|---|
Data de Publicação: | 2023 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/18990 |
Resumo: | In repairable systems, the failure process defined by the failure intensity function can be impacted by three crucial characteristics: the type of repair performed after the failures occur, the underlying cause of the failure (competing risks) and the presence of unobservable factors acting on each failure time or on the system as a whole (unobserved heterogeneity). In particular, unobserved heterogeneity can be modeled by frailty models, well known in the reliability literature. However, the majority of existing studies in this domain assume only minimal repairs after failures, which is a highly restrictive assumption and not always applicable. There is, therefore, a theoretical gap to be explored encompassing frailty models that consider systems subject to both perfect and imperfect repairs and still subject to competing risks. The primary objective of this work is to present new parametric univariate and shared frailty models for multiple repairable systems, considering different types of repairs and a competing risks framework. These proposed models extend and generalize those already existing in the literature, as they account for perfect repairs and all possible failure memories within both the ARA$_m$ and ARI$_m$ classes of imperfect repairs. In this sense, they are models capable of simultaneously identifying the effect of the repairs actions and the presence of unobserved heterogeneity among failure times or among the systems under analysis. This characteristic holds substantial relevance in real-world situations, as a deeper understanding of the system's failure process can lead to improved preventive maintenance policies and reduced repair-related costs. In all proposed models, we assume that the initial failure intensity follows a Power Law Process and that the parametric frailty terms associated with failure times or systems follow a Gamma distribution. We employ a frequentist approach to construct the likelihood function for each model and suggest numerical methods for obtaining maximum likelihood estimators and their corresponding asymptotic confidence intervals. Additionally, we propose the use of Bayesian methodologies based on Markov Chain Monte Carlo algorithms as an alternative to the frequentist method. Simulation studies are conducted for each proposed model, and, finally, the methods presented are applied to real datasets. |
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Brito, Éder Silva deLouzada Neto, Franciscohttp://lattes.cnpq.br/0994050156415890Tomazella, Vera Lucia Damascenohttp://lattes.cnpq.br/8870556978317000http://lattes.cnpq.br/0791900403733039https://orcid.org/0000-0003-3905-1043https://orcid.org/0000-0001-7815-9554https://orcid.org/0000-0002-6780-20892023-12-05T17:12:28Z2023-12-05T17:12:28Z2023-10-09BRITO, Éder Silva de. Reliability analysis of repairable systems considering unobserved heterogeneity and competing risks. 2023. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2023. Disponível em: https://repositorio.ufscar.br/handle/ufscar/18990.https://repositorio.ufscar.br/handle/ufscar/18990In repairable systems, the failure process defined by the failure intensity function can be impacted by three crucial characteristics: the type of repair performed after the failures occur, the underlying cause of the failure (competing risks) and the presence of unobservable factors acting on each failure time or on the system as a whole (unobserved heterogeneity). In particular, unobserved heterogeneity can be modeled by frailty models, well known in the reliability literature. However, the majority of existing studies in this domain assume only minimal repairs after failures, which is a highly restrictive assumption and not always applicable. There is, therefore, a theoretical gap to be explored encompassing frailty models that consider systems subject to both perfect and imperfect repairs and still subject to competing risks. The primary objective of this work is to present new parametric univariate and shared frailty models for multiple repairable systems, considering different types of repairs and a competing risks framework. These proposed models extend and generalize those already existing in the literature, as they account for perfect repairs and all possible failure memories within both the ARA$_m$ and ARI$_m$ classes of imperfect repairs. In this sense, they are models capable of simultaneously identifying the effect of the repairs actions and the presence of unobserved heterogeneity among failure times or among the systems under analysis. This characteristic holds substantial relevance in real-world situations, as a deeper understanding of the system's failure process can lead to improved preventive maintenance policies and reduced repair-related costs. In all proposed models, we assume that the initial failure intensity follows a Power Law Process and that the parametric frailty terms associated with failure times or systems follow a Gamma distribution. We employ a frequentist approach to construct the likelihood function for each model and suggest numerical methods for obtaining maximum likelihood estimators and their corresponding asymptotic confidence intervals. Additionally, we propose the use of Bayesian methodologies based on Markov Chain Monte Carlo algorithms as an alternative to the frequentist method. Simulation studies are conducted for each proposed model, and, finally, the methods presented are applied to real datasets.Em sistemas reparáveis, o processo de falhas definido pela função de intensidade de falhas pode ser impactado por três características importantes: o tipo de reparo realizado após a ocorrência das falhas, a causa que provocou a falha (riscos competitivos) e a existência de fatores não observáveis atuando sobre cada tempo de falha ou sobre o sistema de modo geral (heterogeneidade não observada). Em particular, a heterogeneidade não observada pode ser modelada por modelos de fragilidade, bem conhecidos na literatura de confiabilidade. No entanto, a grande maioria destes trabalhos assume apenas reparos mínimos após as falhas, uma suposição bastante restritiva e nem sempre aplicável. Há, portanto, uma lacuna teórica a ser explorada envolvendo modelos de fragilidade considerando sistemas submetidos a reparos perfeitos e imperfeitos e ainda sujeitos a riscos competitivos. Dessa forma, o principal objetivo deste trabalho é apresentar novos modelos paramétricos de fragilidade univariada e compartilhada para múltiplos sistemas reparáveis sob diferentes tipos de reparo e sob estrutura de riscos competitivos. Os modelos propostos são extensões e generalizações de outros existentes na literatura, pois consideram reparos perfeitos e todas as possíveis memórias de falha para ambas as classes ARA$_m$ e ARI$_m$ de reparo imperfeito. Nesse sentido, são modelos capazes de identificar simultaneamente o efeito dos reparos realizados e a existência de heterogeneidade não observada entre os tempos de falha ou entre os sistemas analisados. Essa característica é bastante relevante para situações do mundo real, pois com maiores informações sobre o processo de falhas de sistemas é possível aprimorar políticas de manutenção preventiva e diminuir custos referentes aos reparos realizados. Em todos os modelos propostos, admitimos que a intensidade inicial de falha segue um Processo de Lei de Potência e que os termos de fragilidade paramétrica associados aos tempos de falha ou aos sistemas seguem uma mesma distribuição Gama. A abordagem frequentista é utilizada para a construção da função de verossimilhança de cada modelo e métodos numéricos são sugeridos para a obtenção dos estimadores de máxima verossimilhança e seus respectivos intervalos de confiança assintóticos. Ainda propomos o uso de metodologias Bayesianas baseadas em algoritmo de Monte Carlo e Cadeias de Markov como alternativa ao método frequentista. Estudos de simulações são realizados para cada modelo proposto e, por fim, os métodos apresentados são sempre aplicados a conjuntos de dados reais.OutraPetrobras - Processo 2017/00732-2engUniversidade Federal de São CarlosCâmpus São CarlosPrograma Interinstitucional de Pós-Graduação em Estatística - PIPGEsUFSCarAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessSistemas reparáveisProcesso de lei de potênciaModelos de fragilidadeHeterogeneidade não observadaRiscos competitivosRepairable systemsPower law processFrailty modelsUnobserved heterogeneityCompeting risksCIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAOReliability analysis of repairable systems considering unobserved heterogeneity and competing risksAnálise de confiabilidade de sistemas reparáveis considerando heterogeneidade não observada e riscos competitivosinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALTese - Éder Brito - PIPGEs - VersãoFinal.pdfTese - Éder Brito - PIPGEs - VersãoFinal.pdfTese Eder Britoapplication/pdf1934844https://repositorio.ufscar.br/bitstream/ufscar/18990/1/Tese%20-%20%c3%89der%20Brito%20-%20PIPGEs%20-%20Vers%c3%a3oFinal.pdf1aec0c2a3f83bdd6772491075f7bc465MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8810https://repositorio.ufscar.br/bitstream/ufscar/18990/2/license_rdff337d95da1fce0a22c77480e5e9a7aecMD52TEXTTese - Éder Brito - PIPGEs - VersãoFinal.pdf.txtTese - Éder Brito - PIPGEs - VersãoFinal.pdf.txtExtracted texttext/plain356762https://repositorio.ufscar.br/bitstream/ufscar/18990/3/Tese%20-%20%c3%89der%20Brito%20-%20PIPGEs%20-%20Vers%c3%a3oFinal.pdf.txtd8d25f2dabd42634af7332fa571d57c5MD53ufscar/189902024-05-14 17:22:30.978oai:repositorio.ufscar.br:ufscar/18990Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222024-05-14T17:22:30Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.eng.fl_str_mv |
Reliability analysis of repairable systems considering unobserved heterogeneity and competing risks |
dc.title.alternative.por.fl_str_mv |
Análise de confiabilidade de sistemas reparáveis considerando heterogeneidade não observada e riscos competitivos |
title |
Reliability analysis of repairable systems considering unobserved heterogeneity and competing risks |
spellingShingle |
Reliability analysis of repairable systems considering unobserved heterogeneity and competing risks Brito, Éder Silva de Sistemas reparáveis Processo de lei de potência Modelos de fragilidade Heterogeneidade não observada Riscos competitivos Repairable systems Power law process Frailty models Unobserved heterogeneity Competing risks CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAO |
title_short |
Reliability analysis of repairable systems considering unobserved heterogeneity and competing risks |
title_full |
Reliability analysis of repairable systems considering unobserved heterogeneity and competing risks |
title_fullStr |
Reliability analysis of repairable systems considering unobserved heterogeneity and competing risks |
title_full_unstemmed |
Reliability analysis of repairable systems considering unobserved heterogeneity and competing risks |
title_sort |
Reliability analysis of repairable systems considering unobserved heterogeneity and competing risks |
author |
Brito, Éder Silva de |
author_facet |
Brito, Éder Silva de |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/0791900403733039 |
dc.contributor.authororcid.por.fl_str_mv |
https://orcid.org/0000-0003-3905-1043 |
dc.contributor.advisor1orcid.por.fl_str_mv |
https://orcid.org/0000-0001-7815-9554 |
dc.contributor.advisor-co1orcid.por.fl_str_mv |
https://orcid.org/0000-0002-6780-2089 |
dc.contributor.author.fl_str_mv |
Brito, Éder Silva de |
dc.contributor.advisor1.fl_str_mv |
Louzada Neto, Francisco |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/0994050156415890 |
dc.contributor.advisor-co1.fl_str_mv |
Tomazella, Vera Lucia Damasceno |
dc.contributor.advisor-co1Lattes.fl_str_mv |
http://lattes.cnpq.br/8870556978317000 |
contributor_str_mv |
Louzada Neto, Francisco Tomazella, Vera Lucia Damasceno |
dc.subject.por.fl_str_mv |
Sistemas reparáveis Processo de lei de potência Modelos de fragilidade Heterogeneidade não observada Riscos competitivos Repairable systems |
topic |
Sistemas reparáveis Processo de lei de potência Modelos de fragilidade Heterogeneidade não observada Riscos competitivos Repairable systems Power law process Frailty models Unobserved heterogeneity Competing risks CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAO |
dc.subject.eng.fl_str_mv |
Power law process Frailty models Unobserved heterogeneity Competing risks |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::REGRESSAO E CORRELACAO |
description |
In repairable systems, the failure process defined by the failure intensity function can be impacted by three crucial characteristics: the type of repair performed after the failures occur, the underlying cause of the failure (competing risks) and the presence of unobservable factors acting on each failure time or on the system as a whole (unobserved heterogeneity). In particular, unobserved heterogeneity can be modeled by frailty models, well known in the reliability literature. However, the majority of existing studies in this domain assume only minimal repairs after failures, which is a highly restrictive assumption and not always applicable. There is, therefore, a theoretical gap to be explored encompassing frailty models that consider systems subject to both perfect and imperfect repairs and still subject to competing risks. The primary objective of this work is to present new parametric univariate and shared frailty models for multiple repairable systems, considering different types of repairs and a competing risks framework. These proposed models extend and generalize those already existing in the literature, as they account for perfect repairs and all possible failure memories within both the ARA$_m$ and ARI$_m$ classes of imperfect repairs. In this sense, they are models capable of simultaneously identifying the effect of the repairs actions and the presence of unobserved heterogeneity among failure times or among the systems under analysis. This characteristic holds substantial relevance in real-world situations, as a deeper understanding of the system's failure process can lead to improved preventive maintenance policies and reduced repair-related costs. In all proposed models, we assume that the initial failure intensity follows a Power Law Process and that the parametric frailty terms associated with failure times or systems follow a Gamma distribution. We employ a frequentist approach to construct the likelihood function for each model and suggest numerical methods for obtaining maximum likelihood estimators and their corresponding asymptotic confidence intervals. Additionally, we propose the use of Bayesian methodologies based on Markov Chain Monte Carlo algorithms as an alternative to the frequentist method. Simulation studies are conducted for each proposed model, and, finally, the methods presented are applied to real datasets. |
publishDate |
2023 |
dc.date.accessioned.fl_str_mv |
2023-12-05T17:12:28Z |
dc.date.available.fl_str_mv |
2023-12-05T17:12:28Z |
dc.date.issued.fl_str_mv |
2023-10-09 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
BRITO, Éder Silva de. Reliability analysis of repairable systems considering unobserved heterogeneity and competing risks. 2023. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2023. Disponível em: https://repositorio.ufscar.br/handle/ufscar/18990. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/18990 |
identifier_str_mv |
BRITO, Éder Silva de. Reliability analysis of repairable systems considering unobserved heterogeneity and competing risks. 2023. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2023. Disponível em: https://repositorio.ufscar.br/handle/ufscar/18990. |
url |
https://repositorio.ufscar.br/handle/ufscar/18990 |
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 |
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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 São Carlos Câmpus São Carlos |
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Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs |
dc.publisher.initials.fl_str_mv |
UFSCar |
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Universidade Federal de São Carlos Câmpus São Carlos |
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UFSCAR |
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