Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process

Detalhes bibliográficos
Autor(a) principal: Almeida, Marco Pollo
Data de Publicação: 2019
Tipo de documento: Tese
Idioma: eng
Título da fonte: Repositório Institucional da UFSCAR
Texto Completo: https://repositorio.ufscar.br/handle/ufscar/11925
Resumo: In this thesis, the main objective is to study certain aspects of modeling failure time data of repairable systems under a competing risks framework. We consider two different models and propose more efficient Bayesian methods for estimating the parameters. In the first model, we discuss inferential procedures based on an objective Bayesian approach for analyzing failures from a single repairable system under independent competing risks. We examined the scenario where a minimal repair is performed at each failure, thereby resulting in that each failure mode appropriately follows a power-law intensity. Besides, it is proposed that the power-law intensity is reparametrized in terms of orthogonal parameters. Then, we derived two objective priors known as the Jeffreys prior and reference prior. Moreover, posterior distributions based on these priors will be obtained in order to find properties which may be optimal in the sense that, for some cases, we prove that these posterior distributions are proper and are also matching priors. In addition, in some cases, unbiased Bayesian estimators of simple closed-form expressions are derived. In the second model, we analyze data from multiple repairable systems under the presence of dependent competing risks. In order to model this dependence structure, we adopted the well-known shared frailty model. This model provides a suitable theoretical basis for generating dependence between the components’ failure times in the dependent competing risks model. It is known that the dependence effect in this scenario influences the estimates of the model parameters. Hence, under the assumption that the cause-specific intensities follow a PLP, we propose a frailty-induced dependence approach to incorporate the dependence among the cause-specific recurrent processes. Moreover, the misspecification of the frailty distribution may lead to errors when estimating the parameters of interest. Because of this, we considered a Bayesian nonparametric approach to model the frailty density in order to offer more flexibility and to provide consistent estimates for the PLP model, as well as insights about heterogeneity among the systems. Both simulation studies and real case studies are provided to illustrate the proposed approaches and demonstrate their validity.
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spelling Almeida, Marco PolloTomazella, Vera Lucia Damascenohttp://lattes.cnpq.br/8870556978317000Avalle, Gustavo Leonel Gilardonihttp://lattes.cnpq.br/6626177394747218http://lattes.cnpq.br/9238886581003630615b1a1d-95f0-4b5f-9c05-15f4012b0c9e2019-10-11T13:20:48Z2019-10-11T13:20:48Z2019-08-30ALMEIDA, Marco Pollo. Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process. 2019. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2019. Disponível em: https://repositorio.ufscar.br/handle/ufscar/11925.https://repositorio.ufscar.br/handle/ufscar/11925In this thesis, the main objective is to study certain aspects of modeling failure time data of repairable systems under a competing risks framework. We consider two different models and propose more efficient Bayesian methods for estimating the parameters. In the first model, we discuss inferential procedures based on an objective Bayesian approach for analyzing failures from a single repairable system under independent competing risks. We examined the scenario where a minimal repair is performed at each failure, thereby resulting in that each failure mode appropriately follows a power-law intensity. Besides, it is proposed that the power-law intensity is reparametrized in terms of orthogonal parameters. Then, we derived two objective priors known as the Jeffreys prior and reference prior. Moreover, posterior distributions based on these priors will be obtained in order to find properties which may be optimal in the sense that, for some cases, we prove that these posterior distributions are proper and are also matching priors. In addition, in some cases, unbiased Bayesian estimators of simple closed-form expressions are derived. In the second model, we analyze data from multiple repairable systems under the presence of dependent competing risks. In order to model this dependence structure, we adopted the well-known shared frailty model. This model provides a suitable theoretical basis for generating dependence between the components’ failure times in the dependent competing risks model. It is known that the dependence effect in this scenario influences the estimates of the model parameters. Hence, under the assumption that the cause-specific intensities follow a PLP, we propose a frailty-induced dependence approach to incorporate the dependence among the cause-specific recurrent processes. Moreover, the misspecification of the frailty distribution may lead to errors when estimating the parameters of interest. Because of this, we considered a Bayesian nonparametric approach to model the frailty density in order to offer more flexibility and to provide consistent estimates for the PLP model, as well as insights about heterogeneity among the systems. Both simulation studies and real case studies are provided to illustrate the proposed approaches and demonstrate their validity.Nesta tese, o objetivo principal é estudar certos aspectos da modelagem de dados de tempo de falha de sistemas reparáveis sob uma estrutura de riscos competitivos. Consideramos dois modelos diferentes e propomos métodos Bayesianos mais eficientes para estimar os parâmetros. No primeiro modelo, discutimos procedimentos inferenciais baseados em uma abordagem Bayesiana objetiva para analisar falhas de um único sistema reparável sob riscos competitivos independentes. Examinamos o cenário em que um reparo mínimo é realizado em cada falha, resultando em que cada modo de falha segue adequadamente uma intensidade de lei de potência. Além disso, propõe-se que a intensidade da lei de potência seja reparametrizada em termos de parâmetros ortogonais. Então, derivamos duas prioris objetivas conhecidas como priori de Jeffreys e priori de referência. Além disso, distribuições posteriores baseadas nessas prioris serão obtidas a fim de encontrar propriedades que podem ser ótimas no sentido de que, em alguns casos, provamos que essas distribuições posteriores são próprias e que também são matching priors. Além disso, em alguns casos, estimadores Bayesianos não-viesados de forma fechada são derivados. No segundo modelo, analisamos dados de múltiplos sistemas reparáveis sob a presença de riscos competitivos dependentes. Para modelar essa estrutura de dependência, adotamos o conhecido modelo de fragilidade compartilhada. Esse modelo fornece uma base teórica adequada para gerar dependência entre os tempos de falha dos componentes no modelo de riscos competitivos dependentes. Sabe-se que o efeito de dependência neste cenário influencia as estimativas dos parâmetros do modelo. Assim, sob o pressuposto de que as intensidades específicas de causa seguem um PLP, propomos uma abordagem de dependência induzida pela fragilidade para incorporar a dependência entre os processos recorrentes específicos da causa. Além disso, a especificação incorreta da distribuição de fragilidade pode levar a erros na estimativa dos parâmetros de interesse. Por isso, consideramos uma abordagem Bayesiana não paramétrica para modelar a densidade da fragilidade, a fim de oferecer mais flexibilidade e fornecer estimativas consistentes para o modelo PLP, bem como insights sobre a heterogeneidade entre os sistemas. São fornecidos estudos de simulação e estudos de casos reais para ilustrar as abordagens propostas e demonstrar sua validade.Não recebi financiamentoengUniversidade 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/openAccessRiscos competitivosProcesso de lei de potenciaProcesso de Poisson não-homogêneoInferência BayesianaSistemas reparáveisCompeting risksPower-law processNon-homogeneous Poisson processBayesian inferenceRepairable systemCIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICACIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA NAO-PARAMETRICACIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA PARAMETRICAStatistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law processInferência estatística para processo de Poisson não-homogêneo com riscos competitivos: uma abordagem de sistemas reparáveis sob processo de lei de potênciainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis600ceb2c79a-7b68-4784-a3a7-b6fb90af1437reponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufscar.br/bitstream/ufscar/11925/3/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD53ORIGINALThesis_final_version_Marco_Pollo_Almeida_PIPGES.pdfThesis_final_version_Marco_Pollo_Almeida_PIPGES.pdfapplication/pdf2412189https://repositorio.ufscar.br/bitstream/ufscar/11925/1/Thesis_final_version_Marco_Pollo_Almeida_PIPGES.pdf0e0ea77eb2c6a89a1db09352e879ad1bMD51CartaComprovVersFinal_Marco_Pollo_PIPGES.pdfCartaComprovVersFinal_Marco_Pollo_PIPGES.pdfapplication/pdf536841https://repositorio.ufscar.br/bitstream/ufscar/11925/2/CartaComprovVersFinal_Marco_Pollo_PIPGES.pdf493b54c92711c27e218416391996422bMD52TEXTThesis_final_version_Marco_Pollo_Almeida_PIPGES.pdf.txtThesis_final_version_Marco_Pollo_Almeida_PIPGES.pdf.txtExtracted texttext/plain206897https://repositorio.ufscar.br/bitstream/ufscar/11925/4/Thesis_final_version_Marco_Pollo_Almeida_PIPGES.pdf.txtd1ed6ad29ed5cb4e3acee8b6e2541c37MD54CartaComprovVersFinal_Marco_Pollo_PIPGES.pdf.txtCartaComprovVersFinal_Marco_Pollo_PIPGES.pdf.txtExtracted texttext/plain1https://repositorio.ufscar.br/bitstream/ufscar/11925/6/CartaComprovVersFinal_Marco_Pollo_PIPGES.pdf.txt68b329da9893e34099c7d8ad5cb9c940MD56THUMBNAILThesis_final_version_Marco_Pollo_Almeida_PIPGES.pdf.jpgThesis_final_version_Marco_Pollo_Almeida_PIPGES.pdf.jpgIM Thumbnailimage/jpeg8025https://repositorio.ufscar.br/bitstream/ufscar/11925/5/Thesis_final_version_Marco_Pollo_Almeida_PIPGES.pdf.jpgc6dd83416372f7ef08f30ad759a9c4baMD55CartaComprovVersFinal_Marco_Pollo_PIPGES.pdf.jpgCartaComprovVersFinal_Marco_Pollo_PIPGES.pdf.jpgIM Thumbnailimage/jpeg12545https://repositorio.ufscar.br/bitstream/ufscar/11925/7/CartaComprovVersFinal_Marco_Pollo_PIPGES.pdf.jpg8ba41c495f5949782d48d879bfadb5b5MD57ufscar/119252023-09-18 18:32:00.998oai:repositorio.ufscar.br:ufscar/11925Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:32Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false
dc.title.eng.fl_str_mv Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process
dc.title.alternative.por.fl_str_mv Inferência estatística para processo de Poisson não-homogêneo com riscos competitivos: uma abordagem de sistemas reparáveis sob processo de lei de potência
title Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process
spellingShingle Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process
Almeida, Marco Pollo
Riscos competitivos
Processo de lei de potencia
Processo de Poisson não-homogêneo
Inferência Bayesiana
Sistemas reparáveis
Competing risks
Power-law process
Non-homogeneous Poisson process
Bayesian inference
Repairable system
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA NAO-PARAMETRICA
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA PARAMETRICA
title_short Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process
title_full Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process
title_fullStr Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process
title_full_unstemmed Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process
title_sort Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process
author Almeida, Marco Pollo
author_facet Almeida, Marco Pollo
author_role author
dc.contributor.authorlattes.por.fl_str_mv http://lattes.cnpq.br/9238886581003630
dc.contributor.author.fl_str_mv Almeida, Marco Pollo
dc.contributor.advisor1.fl_str_mv Tomazella, Vera Lucia Damasceno
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/8870556978317000
dc.contributor.advisor-co1.fl_str_mv Avalle, Gustavo Leonel Gilardoni
dc.contributor.advisor-co1Lattes.fl_str_mv http://lattes.cnpq.br/6626177394747218
dc.contributor.authorID.fl_str_mv 615b1a1d-95f0-4b5f-9c05-15f4012b0c9e
contributor_str_mv Tomazella, Vera Lucia Damasceno
Avalle, Gustavo Leonel Gilardoni
dc.subject.por.fl_str_mv Riscos competitivos
Processo de lei de potencia
Processo de Poisson não-homogêneo
Inferência Bayesiana
Sistemas reparáveis
topic Riscos competitivos
Processo de lei de potencia
Processo de Poisson não-homogêneo
Inferência Bayesiana
Sistemas reparáveis
Competing risks
Power-law process
Non-homogeneous Poisson process
Bayesian inference
Repairable system
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA NAO-PARAMETRICA
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA PARAMETRICA
dc.subject.eng.fl_str_mv Competing risks
Power-law process
Non-homogeneous Poisson process
Bayesian inference
Repairable system
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA NAO-PARAMETRICA
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::ESTATISTICA::INFERENCIA PARAMETRICA
description In this thesis, the main objective is to study certain aspects of modeling failure time data of repairable systems under a competing risks framework. We consider two different models and propose more efficient Bayesian methods for estimating the parameters. In the first model, we discuss inferential procedures based on an objective Bayesian approach for analyzing failures from a single repairable system under independent competing risks. We examined the scenario where a minimal repair is performed at each failure, thereby resulting in that each failure mode appropriately follows a power-law intensity. Besides, it is proposed that the power-law intensity is reparametrized in terms of orthogonal parameters. Then, we derived two objective priors known as the Jeffreys prior and reference prior. Moreover, posterior distributions based on these priors will be obtained in order to find properties which may be optimal in the sense that, for some cases, we prove that these posterior distributions are proper and are also matching priors. In addition, in some cases, unbiased Bayesian estimators of simple closed-form expressions are derived. In the second model, we analyze data from multiple repairable systems under the presence of dependent competing risks. In order to model this dependence structure, we adopted the well-known shared frailty model. This model provides a suitable theoretical basis for generating dependence between the components’ failure times in the dependent competing risks model. It is known that the dependence effect in this scenario influences the estimates of the model parameters. Hence, under the assumption that the cause-specific intensities follow a PLP, we propose a frailty-induced dependence approach to incorporate the dependence among the cause-specific recurrent processes. Moreover, the misspecification of the frailty distribution may lead to errors when estimating the parameters of interest. Because of this, we considered a Bayesian nonparametric approach to model the frailty density in order to offer more flexibility and to provide consistent estimates for the PLP model, as well as insights about heterogeneity among the systems. Both simulation studies and real case studies are provided to illustrate the proposed approaches and demonstrate their validity.
publishDate 2019
dc.date.accessioned.fl_str_mv 2019-10-11T13:20:48Z
dc.date.available.fl_str_mv 2019-10-11T13:20:48Z
dc.date.issued.fl_str_mv 2019-08-30
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 ALMEIDA, Marco Pollo. Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process. 2019. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2019. Disponível em: https://repositorio.ufscar.br/handle/ufscar/11925.
dc.identifier.uri.fl_str_mv https://repositorio.ufscar.br/handle/ufscar/11925
identifier_str_mv ALMEIDA, Marco Pollo. Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process. 2019. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2019. Disponível em: https://repositorio.ufscar.br/handle/ufscar/11925.
url https://repositorio.ufscar.br/handle/ufscar/11925
dc.language.iso.fl_str_mv eng
language eng
dc.relation.confidence.fl_str_mv 600
dc.relation.authority.fl_str_mv ceb2c79a-7b68-4784-a3a7-b6fb90af1437
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 São Carlos
Câmpus São Carlos
dc.publisher.program.fl_str_mv Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs
dc.publisher.initials.fl_str_mv UFSCar
publisher.none.fl_str_mv Universidade Federal de São Carlos
Câmpus São Carlos
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