Submitted by Pedro Barros (pedro.silvabarros@ufpe.br) on 2018-06-29T19:10:32Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) DISSERTAÇÃO Thaís Lima Corrêa.pdf: 1826347 bytes, checksum: 3e2a4eaa7d0d1c4c2e98d8d8e9bec071 (MD5) / Made available in DSpace on 2018-06-29T19:10:32Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) DISSERTAÇÃO Thaís Lima Corrêa.pdf: 1826347 bytes, checksum: 3e2a4eaa7d0d1c4c2e98d8d8e9bec071 (MD5) Previous issue date: 2017-02-21 / CAPES / 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. / O 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.

Submitted by Mario BC (mario@bc.ufrpe.br) on 2018-05-15T13:58:25Z No. of bitstreams: 1 Ricardo Jose Ferreira.pdf: 1514159 bytes, checksum: 365dd17d70da575c6399efe53acf1631 (MD5) / Made available in DSpace on 2018-05-15T13:58:25Z (GMT). No. of bitstreams: 1 Ricardo Jose Ferreira.pdf: 1514159 bytes, checksum: 365dd17d70da575c6399efe53acf1631 (MD5) Previous issue date: 2016-01-29 / In order to analyze interventions in repairable systems, the literature contains several methodologies aiming to model the behavior of times between interventions. Such interventions can be modeled by Point Stochastic Processes in order to analyze the probabilistic behavior of times between events. Specifically, the Generalized Renewal Processes allow the study of times between interventions by measuring the quality of each intervention and the response of the system to these interventions — this is done by using the concept of virtual age. In such concept it is possible to apply two kinds of Kijima models (Type I and II). Therefore, this work presents a model capable of study the quality of interventions using up of a mix between the two Kijima models where it is possible to capture the performance on each of these interventions proportionally. Specifically, a new approach to virtual age of Kijima models is presented as well as mathematical properties of the Generalized Renewal Process using the Weibull distribution probability. Finally, the applicability of the model is checked in real data from some problems found in the literature. / Para analisar intervenções em sistemas reparáveis, a literatura apresenta diversas metodologias visando modelar o comportamento de tempos entre intervenções. Tais intervenções podem ser modeladas por Processos Estocásticos Pontuais visando analisar o comportamento probabilístico dos tempos entre eventos. Especificamente, os Processos de Renovação Generalizados permitem o estudo de tempos entre intervenções medindo a qualidade de impacto de cada intervenção e a resposta do sistema a tais intervenções - isto é feito utilizando o conceito de idade virtual. Em tal conceito é possível se aplicar dois tipos de modelos Kijima (tipo I e II).Sendo assim, esse trabalho apresenta um modelo capaz de estudar a qualidade de intervenções utilizando-se de uma mistura entre os dois modelos Kijima onde é possível capturar a atuação de cada um desses sobre as intervenções proporcionalmente. Especificamente, uma nova abordagem sobre a idade virtual dos modelos Kijima é apresentada, bem como propriedades matemáticas dos Processos de Renovação Generalizados utilizando a distribuição de probabilidadeWeibull. Por fim, a aplicabilidade do modelo é verificada em dados reais de alguns problemas presentes na literatura.

We consider a class of periodic preventive maintenance (PM) optimization problems, for a single piece of equipment that deteriorates with time or use, and can be repaired upon failure, through corrective maintenance (CM). We develop analytical and simulation-based optimization models that seek an optimal periodic PM policy, which minimizes the sum of the expected total cost of PMs and the risk-averse cost of CMs, over a finite planning horizon. In the simulation-based models, we assume that both types of maintenance actions are imperfect, whereas our analytical models consider imperfect PMs with minimal CMs. The effectiveness of maintenance actions is modeled using age reduction factors. For a repairable unit of equipment, its virtual age, and not its calendar age, determines the associated failure rate. Therefore, two sets of parameters, one describing the effectiveness of maintenance actions, and the other that defines the underlying failure rate of a piece of equipment, are critical to our models. Under a given maintenance policy, the two sets of parameters and a virtual-age-based age-reduction model, completely define the failure process of a piece of equipment. In practice, the true failure rate, and exact quality of the maintenance actions, cannot be determined, and are often estimated from the equipment failure history. We use a Bayesian approach to parameter estimation, under which a random-walk-based Gibbs sampler provides posterior estimates for the parameters of interest. Our posterior estimates for a few datasets from the literature, are consistent with published results. Furthermore, our computational results successfully demonstrate that our Gibbs sampler is arguably the obvious choice over a general rejection sampling-based parameter estimation method, for this class of problems. We present a general simulation-based periodic PM optimization model, which uses the posterior estimates to simulate the number of operational equipment failures, under a given periodic PM policy. Optimal periodic PM policies, under the classical maximum likelihood (ML) and Bayesian estimates are obtained for a few datasets. Limitations of the ML approach are revealed for a dataset from the literature, in which the use of ML estimates of the parameters, in the maintenance optimization model, fails to capture a trivial optimal PM policy. Finally, we introduce a single-stage and a two-stage formulation of the risk-averse periodic PM optimization model, with imperfect PMs and minimal CMs. Such models apply to a class of complex equipment with many parts, operational failures of which are addressed by replacing or repairing a few parts, thereby not affecting the failure rate of the equipment under consideration. For general values of PM age reduction factors, we provide sufficient conditions to establish the convexity of the first and second moments of the number of failures, and the risk-averse expected total maintenance cost, over a finite planning horizon. For increasing Weibull rates and a general class of increasing and convex failure rates, we show that these convexity results are independent of the PM age reduction factors. In general, the optimal periodic PM policy under the single-stage model is no better than the optimal two-stage policy. But if PMs are assumed perfect, then we establish that the single-stage and the two-stage optimization models are equivalent. / text