The maintenance cost for an engineering system is an uncertain quantity due to uncertainties associated with occurrence of failure and the time taken to restore the system. The problem of probabilistic analysis of maintenance cost can be modeled as a stochastic renewal-reward process, which is a complex problem. Assuming that the time horizon of the maintenance policy approaches infinity, simple asymptotic formulas have been derived for the failure rate and the cost per unit time. These asymptotic formulas are widely utilized in the reliability literature for the optimization of a maintenance policy. However, in the finite life of highly reliable systems, such as safety systems used in a nuclear plant, the applicability of asymptotic approximations is questionable. Thus, the development of methods for accurate evaluation of expected maintenance cost, failure rate, and availability of engineering systems is the subject matter of this thesis. In this thesis, an accurate derivation of any m-th order statistical moment of maintenance cost is presented. The proposed formulation can be used to derive results for a specific maintenance policy. The cost of condition-based maintenance (CBM) of a system is analyzed in detail, in which the system degradation is modeled as a stochastic gamma process. The CBM model is generalized by considering the random repair time and delay in degradation initiation. Since the expected cost is not informative enough to estimate the financial risk measures, such as Value-at-Risk, the probability distribution of the maintenance cost is derived. This derivation is based on an interesting idea that the characteristic function of the cost can be computed from a renewal-type integral equation, and its Fourier transform leads to the probability distribution. A sequential inspection and replacement strategy is presented for the asset management of a large population of components. The finite-time analyses presented in this thesis can be combined to compute the reliability and availability at the system level. Practical case studies involving the maintenance of the heat transport piping system in a nuclear plant and a breakwater are presented. A general conclusion is that finite time cost analysis should be used for a realistic evaluation and optimization of maintenance policies for critical infrastructure systems.

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.

A quasi-renewal process is more realistic in modeling the behavior of a repairable system than traditional models such as perfect repair and minimal repair since it reflects the deterioration process of the system over time while traditional models do not. The quasi-renewal parameter is set to a value between 0 and 1 to indicate the rate of deterioration. Moreover, a quasi-renewal process can also be used to model the increasing time of maintenance actions due to the increasing difficulty of maintaining an aging system by setting the parameter to a value larger than 1. We construct a model where the operating times follow a quasi-renewal process and the corrective/preventive maintenance times follow another quasi-renewal process. A quasi-renewal function and two equivalent point availability expressions are developed for the model described by a quasi-renewal process with and age-dependent preventive maintenance policy. In addition, numerical results from various theoretical distributions are obtained to illustrate the behavior of the models. The two equivalent point availability functions each contains an infinite sum and must be truncated to obtain a numerical approximation. The two approximated point availability functions form upper and lower bounds on the real value. The bounds are useful for determining the result accuracy, which can be arbitrarily increased by adding more terms to the truncated summation. Our framework provides a new time-dependent availability model for a non-stationary process with a preventive maintenance policy without any cost structure or optimization problem. / Ph. D.

This dissertation develops a novel method to detect clusters that appear in financial transaction data that are linked to fraud. The methods utilize properties of order statistics, renewal processes, and model segmentation. We apply the Minimum Description Length (MDL) principle to select the best model. Our technique makes use of a genetic algorithm to determine the number and location of anomalous cluster(s) embedded in a set of financial transactions. We apply our novel cluster detection method to the Paycheck Protection Program (PPP), a U.S. Government initiative launched in April 2020 amid the COVID-19 pandemic to aid small businesses affected by the crisis. A total of 11.46 million loans amounting to $796 billion were approved under the program.

Submitted by admin tede (tede@pucgoias.edu.br) on 2017-08-21T12:30:58Z No. of bitstreams: 1 Celso Aurélio de Morais Lima.pdf: 2546394 bytes, checksum: 8a8908066e6f60ae202da67d1738b90d (MD5) / Made available in DSpace on 2017-08-21T12:30:58Z (GMT). No. of bitstreams: 1 Celso Aurélio de Morais Lima.pdf: 2546394 bytes, checksum: 8a8908066e6f60ae202da67d1738b90d (MD5) Previous issue date: 2017-04-27 / The main objective of this dissertation is to develop a reliability assessment applied to reparable systems in the sugar and alcohol industry. The work has a quantitative approach with a combined research method: simulation modeling with case-study. Therefore, a dynamic modeling is used to develop a case-study. For this, a Non- Homogeneous Markov Process (PNHM) model is used to represent the states transitions (operation-maintenance) of sugar centrifuges, in order to obtain reliability indicators. Integrated to the PNHM model, it will be used the Generalized Renewal Process (PRG) to describe the probabilities of failures considering imperfect repairs. The PRG is defined according to the parameters of scale, shape and rejuvenation (α, β, q), which are estimated by Bayesian Inference. In the development of the case-study, the data collection of centrifugal failures was performed and, through the simulation of the hybrid model, the case-study was conceived. The estimated availability for 5640 hours was 93.23%, whose the other 7% represents maintenances moments. For 323 hours of simulation, the reliability resulting was 50%, demonstrating high system susceptibility to failures. The results suggest the revisions of the intervals defined for preventives maintenances, which should be applied to the most observed failure mode, called malfunction of the sensing systems. / O principal objetivo desta dissertação é desenvolver uma avaliação de confiabilidade aplicada a sistemas reparáveis, na indústria sucroalcooleira. O trabalho possui abordagem quantitativa com método de pesquisa combinado: modelagem de simulação com estudo de caso. Portanto, utilizar-se-á de uma modelagem dinâmica para desenvolver um estudo de caso. Para isso, aplicar-se-á um modelo de Processos Não Homogêneos de Markov (PNHM) para representar as transições entre estados (operacional-em manutenção) das centrífugas de açúcar, visando obter indicadores de confiabilidade. Integrado ao modelo PNHM, será utilizado o Processo de Renovação Generalizado (PRG) para descrever as probabilidades de falhas considerando reparos imperfeitos. O PRG é definido em função dos parâmetros de escala, forma e rejuvenescimento ( ,!,"), que serão estimados via Inferência Bayesiana. No desenvolvimento do estudo de caso, realizou-se a coleta de dados de falhas das centrífugas e, por meio da simulação do modelo híbrido, o estudo de caso foi concebido. A disponibilidade estimada para 5640 horas foi de 93,23%, sendo os 7% complementares referentes a manutenções. A confiabilidade apresentada foi de 50% para 323 horas, demonstrando alta suscetibilidade do sistema à falhas. Os resultados sugerem revisão nos intervalos definidos para manutenção preventiva, as quais deverão ser dedicadas ao modo de falha mais observado, denominado mal funcionamento dos sistemas de sensoreamento.

在本文中，我們證明了：若對應於壽命分佈函數F之更新函數為凸（ 凹 ）族，因此解決了Shaked和Zhu(1992)所提出的兩個問題。 蝻う漫宒銵A 我們進一步得到了於某些特定之壽命分佈函數族中， / We prove that if the renewal function M(t) corresponding to a life distribution F is convex(resp. concave) then F is NBU(resp. NWU), and hence answer two questions posed by Shaked and Zhu(1992). Moreover, based on the renewal function, some characterizations of the exponential distribution within certain classes of life distributions are given. Key words and phrases:exponential distribution;renewal counting process; DFR;NBU;NWU;NBUE;NWUE.

This thesis deals with the reliability and maintenance of structures that are damaged by shocks arriving randomly in time. The degradation is modeled as a cumulative stochastic point process. Previous studies mostly adopted expected cost rate criterion for optimizing the maintenance policies, which ignores practical implications of discounting of maintenance cost over the life cycle of the system.Therefore, detailed analysis of expected discounted cost criterion has been done, which provides a more realistic basis for optimizing the maintenance. Examples of maintenance policies combining preventive maintenance with age- based replacement are analyzed. Derivation for general cases involving preventive maintenance damage level have been discussed. Special cases are also considered.

This thesis deals with the reliability and maintenance of structures that are damaged by shocks arriving randomly in time. The degradation is modeled as a cumulative stochastic point process. Previous studies mostly adopted expected cost rate criterion for optimizing the maintenance policies, which ignores practical implications of discounting of maintenance cost over the life cycle of the system.Therefore, detailed analysis of expected discounted cost criterion has been done, which provides a more realistic basis for optimizing the maintenance. Examples of maintenance policies combining preventive maintenance with age- based replacement are analyzed. Derivation for general cases involving preventive maintenance damage level have been discussed. Special cases are also considered.

We study the properties of thinning and Markov chain thinning of renewal processes. Among others, we investigate whether some special renewal processes can be obtained through Markov chain thinning.

There are two main parts in this thesis. The first one concerns valvometry, which is here the study of the distance between both parts of the shell of an oyster, over time. The health status of oysters can be characterized using valvometry in order to obtain insights about the quality of their environment. We consider that a renewal process with four states underlies the behaviour of the studied oysters. Such a hidden process can be retrieved from a valvometric signal by assuming that some probability density function linked with this signal, is bimodal. We then compare several estimators which take this assumption into account, including kernel density estimators.In another chapter, we compare several regression approaches, aiming at analysing transcriptomic data. To understand which explanatory variables have an effect on gene expressions, we apply a multiple testing procedure on these data, through the linear model FAMT. The SIR method may find nonlinear relations in such a context. It is however more commonly used when the response variable is univariate. A multivariate version of SIR was then developed. Procedures to measure gene expressions can be expensive. The sample size n of the corresponding datasets is then often small. That is why we also studied SIR when n is less than the number of explanatory variables p.