Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process
Autor(a) principal: | |
---|---|
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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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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UFSCAR |
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UFSCAR |
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