Some Properties of Weighted Distributions in the Context of Repairable Systems

In this article we introduce some structural relationships between weighted and original variables in the context of maintainability function and reversed repair rate. Furthermore, we prove some characterization theorems for specific models such as power, exponential, Pareto II, beta, and Pearson system of distributions using the relationships between the original and weighted random variables

Asset health prediction using the explicit hazard model

The ability to estimate the asset reliability and the probability of failure is critical to reducing maintenance costs, operation downtime, and safety hazards. Predicting the survival time and the probability of failure in future time is an indispensable requirement in prognostics and asset health management. In traditional reliability models, the lifetime of an asset is estimated using failure event data, alone; however, statistically sufficient failure event data are often difficult to attain in real-life situations due to poor data management, effective preventive maintenance, and the small population of identical assets in use. Condition indicators and operating environment indicators are two types of covariate data that are normally obtained in addition to failure event and suspended data. These data contain significant information about the state and health of an asset. Condition indicators reflect the level of degradation of assets while operating environment indicators accelerate or decelerate the lifetime of assets. When these data are available, an alternative approach to the traditional reliability analysis is the modelling of condition indicators and operating environment indicators and their failure-generating mechanisms using a covariate-based hazard model. The literature review indicates that a number of covariate-based hazard models have been developed. All of these existing covariate-based hazard models were developed based on the principle theory of the Proportional Hazard Model (PHM). However, most of these models have not attracted much attention in the field of machinery prognostics. Moreover, due to the prominence of PHM, attempts at developing alternative models, to some extent, have been stifled, although a number of alternative models to PHM have been suggested. The existing covariate-based hazard models neglect to fully utilise three types of asset health information (including failure event data (i.e. observed and/or suspended), condition data, and operating environment data) into a model to have more effective hazard and reliability predictions. In addition, current research shows that condition indicators and operating environment indicators have different characteristics and they are non-homogeneous covariate data. Condition indicators act as response variables (or dependent variables) whereas operating environment indicators act as explanatory variables (or independent variables). However, these non-homogenous covariate data were modelled in the same way for hazard prediction in the existing covariate-based hazard models. The related and yet more imperative question is how both of these indicators should be effectively modelled and integrated into the covariate-based hazard model. This work presents a new approach for addressing the aforementioned challenges. The new covariate-based hazard model, which termed as Explicit Hazard Model (EHM), explicitly and effectively incorporates all three available asset health information into the modelling of hazard and reliability predictions and also drives the relationship between actual asset health and condition measurements as well as operating environment measurements. The theoretical development of the model and its parameter estimation method are demonstrated in this work. EHM assumes that the baseline hazard is a function of the both time and condition indicators. Condition indicators provide information about the health condition of an asset; therefore they update and reform the baseline hazard of EHM according to the health state of asset at given time t. Some examples of condition indicators are the vibration of rotating machinery, the level of metal particles in engine oil analysis, and wear in a component, to name but a few. Operating environment indicators in this model are failure accelerators and/or decelerators that are included in the covariate function of EHM and may increase or decrease the value of the hazard from the baseline hazard. These indicators caused by the environment in which an asset operates, and that have not been explicitly identified by the condition indicators (e.g. Loads, environmental stresses, and other dynamically changing environment factors). While the effects of operating environment indicators could be nought in EHM; condition indicators could emerge because these indicators are observed and measured as long as an asset is operational and survived. EHM has several advantages over the existing covariate-based hazard models. One is this model utilises three different sources of asset health data (i.e. population characteristics, condition indicators, and operating environment indicators) to effectively predict hazard and reliability. Another is that EHM explicitly investigates the relationship between condition and operating environment indicators associated with the hazard of an asset. Furthermore, the proportionality assumption, which most of the covariate-based hazard models suffer from it, does not exist in EHM. According to the sample size of failure/suspension times, EHM is extended into two forms: semi-parametric and non-parametric. The semi-parametric EHM assumes a specified lifetime distribution (i.e. Weibull distribution) in the form of the baseline hazard. However, for more industry applications, due to sparse failure event data of assets, the analysis of such data often involves complex distributional shapes about which little is known. Therefore, to avoid the restrictive assumption of the semi-parametric EHM about assuming a specified lifetime distribution for failure event histories, the non-parametric EHM, which is a distribution free model, has been developed. The development of EHM into two forms is another merit of the model. A case study was conducted using laboratory experiment data to validate the practicality of the both semi-parametric and non-parametric EHMs. The performance of the newly-developed models is appraised using the comparison amongst the estimated results of these models and the other existing covariate-based hazard models. The comparison results demonstrated that both the semi-parametric and non-parametric EHMs outperform the existing covariate-based hazard models. Future research directions regarding to the new parameter estimation method in the case of time-dependent effects of covariates and missing data, application of EHM in both repairable and non-repairable systems using field data, and a decision support model in which linked to the estimated reliability results, are also identified.

Desenvolvimento de modelo para a melhoria do planeamento da manutenção

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Mecânica

Characterizations of distributions using log odds rate

In this paper, we examine the relationships between log odds rate and various reliability measures such as hazard rate and reversed hazard rate in the context of repairable systems. We also prove characterization theorems for some families of distributions viz. Burr, Pearson and log exponential models. We discuss the properties and applications of log odds rate in weighted models. Further we extend the concept to the bivariate set up and study its properties.

A novel repair model for imperfect maintenance

Commonly used repair rate models for repairable systems in the reliability literature are renewal processes, generalised renewal processes or non-homogeneous Poisson processes. In addition to these models, geometric processes (GP) are studied occasionally. The GP, however, can only model systems with monotonously changing (increasing, decreasing or constant) failure intensities. This paper deals with the reliability modelling of failure processes for repairable systems where the failure intensity shows a bathtub-type non-monotonic behaviour. A new stochastic process, i.e. an extended Poisson process, is introduced in this paper. Reliability indices are presented, and the parameters of the new process are estimated. Experimental results on a data set demonstrate the validity of the new process.

A novel repair model for imperfect maintenance

The basic repair rate models for repairable systems may be homogeneous Poisson processes, renewal processes or nonhomogeneous Poisson processes. In addition to these models, geometric processes are studied occasionally. Geometric processes, however, can only model systems with monotonously changing (increasing, decreasing or constant) failure intensity. This paper deals with the reliability modelling of the failure process of repairable systems when the failure intensity shows a bathtub type non-monotonic behaviour. A new stochastic process, an extended Poisson process, is introduced. Reliability indices and parameter estimation are presented. A comparison of this model with other repair models based on a dataset is made.

Modelagem da disponibilidade de uma unidade geradora da UHE-Tucuruí

Com o advindo do marco regulatório do Setor Elétrico Brasileiro, a partir de 2004, os agentes que atuam neste mercado têm experimentado um acirramento nas disputas por novos negócios, evidenciando um aumento de competitividade. A Disponibilidade dos Ativos Físicos e os Custos com Manutenção se apresentam como os pontos chave para a competitividade dos agentes. O presente trabalho tem por objetivo apresentar uma metodologia de Análise de Disponibilidade de Sistemas Reparáveis, durante as etapas de projeto ou de operação do sistema, contemplando a mensuração dos Custos com Manutenção versus o Desembolso com Aquisição para um nível esperado de desempenho. A metodologia para a Análise de Disponibilidade sugerida se utiliza da construção do Diagrama de Blocos do Sistema com respectivas descrições funcionais, exportação das informações para o formato de Árvore de Sucesso, composta de portas lógicas dos tipos "E" e "OU" as quais caracterizam um subsistema integrante do sistema principal. O analista pode reavaliar a topologia do sistema, agregando ou retirando redundâncias com a finalidade de ajustar o desempenho do projeto aos requisitos de Disponibilidade, Custo de Aquisição e Custos de Manutenção. Como resultados do trabalho foram identificadas lacunas normativas que definem a forma de controle do desempenho dos ativos, estabelecida uma sistemática de integração entre técnicas de modelagem de confiabilidade e disponibilidade, estabelecidos e incorporados indicadores de desempenho de Manutenção Programada em um agente do mercado, foram modelados e discutidos diferentes cenários para um Sistema de Circulação de Óleo de Mancal e foi aplicado o modelo a toda uma Unidade Geradora Hidráulica por meio da implementação computacional do modelo aos componentes críticos dos principais sistemas.

Reliability analysis and economic equipment replacement appraisal for substation and sub-transmission systems with explicit inclusion of non-repairable failures

The modern society has come to expect the electrical energy on demand, while many of the facilities in power systems are aging beyond repair and maintenance. The risk of failure is increasing with the aging equipments and can pose serious consequences for continuity of electricity supply. As the equipments used in high voltage power networks are very expensive, economically it may not be feasible to purchase and store spares in a warehouse for extended periods of time. On the other hand, there is normally a significant time before receiving equipment once it is ordered. This situation has created a considerable interest in the evaluation and application of probability methods for aging plant and provisions of spares in bulk supply networks, and can be of particular importance for substations. Quantitative adequacy assessment of substation and sub-transmission power systems is generally done using a contingency enumeration approach which includes the evaluation of contingencies, classification of the contingencies based on selected failure criteria. The problem is very complex because of the need to include detailed modelling and operation of substation and sub-transmission equipment using network flow evaluation and to consider multiple levels of component failures. In this thesis a new model associated with aging equipment is developed to combine the standard tools of random failures, as well as specific model for aging failures. This technique is applied in this thesis to include and examine the impact of aging equipments on system reliability of bulk supply loads and consumers in distribution network for defined range of planning years. The power system risk indices depend on many factors such as the actual physical network configuration and operation, aging conditions of the equipment, and the relevant constraints. The impact and importance of equipment reliability on power system risk indices in a network with aging facilities contains valuable information for utilities to better understand network performance and the weak links in the system. In this thesis, algorithms are developed to measure the contribution of individual equipment to the power system risk indices, as part of the novel risk analysis tool. A new cost worth approach was developed in this thesis that can make an early decision in planning for replacement activities concerning non-repairable aging components, in order to maintain a system reliability performance which economically is acceptable. The concepts, techniques and procedures developed in this thesis are illustrated numerically using published test systems. It is believed that the methods and approaches presented, substantially improve the accuracy of risk predictions by explicit consideration of the effect of equipment entering a period of increased risk of a non-repairable failure.

Failure analysis of engineering systems with preventive maintenance and failure interactions

Optimal operation and maintenance of engineering systems heavily rely on the accurate prediction of their failures. Most engineering systems, especially mechanical systems, are susceptible to failure interactions. These failure interactions can be estimated for repairable engineering systems when determining optimal maintenance strategies for these systems. An extended Split System Approach is developed in this paper. The technique is based on the Split System Approach and a model for interactive failures. The approach was applied to simulated data. The results indicate that failure interactions will increase the hazard of newly repaired components. The intervals of preventive maintenance actions of a system with failure interactions, will become shorter compared with scenarios where failure interactions do not exist.

Seismic performance of hybrid fiber reinforced polymer-concrete pier frame systems

As an alternative to transverse spiral or hoop steel reinforcement, fiber reinforced polymers (FRPs) were introduced to the construction industry in the 1980’s. The concept of concrete-filled FRP tube (CFFT) has raised great interest amongst researchers in the last decade. FRP tube can act as a pour form, protective jacket, and shear and flexural reinforcement for concrete. However, seismic performance of CFFT bridge substructure has not yet been fully investigated. Experimental work in this study included four two-column bent tests, several component tests and coupon tests. Four 1/6-scale bridge pier frames, consisting of a control reinforced concrete frame (RCF), glass FRP-concrete frame (GFF), carbon FRP-concrete frame (CFF), and hybrid glass/carbon FRP-concrete frame (HFF) were tested under reverse cyclic lateral loading with constant axial loads. Specimen GFF did not show any sign of cracking at a drift ratio as high as 15% with considerable loading capacity, whereas Specimen CFF showed that lowest ductility with similar load capacity as in Specimen GFF. FRP-concrete columns and pier cap beams were then cut from the pier frame specimens, and were tested again in three point flexure under monotonic loading with no axial load. The tests indicated that bonding between FRP and concrete and yielding of steel both affect the flexural strength and ductility of the components. The coupon tests were carried out to establish the tensile strength and elastic modulus of each FRP tube and the FRP mold for the pier cap beam in the two principle directions of loading. A nonlinear analytical model was developed to predict the load-deflection responses of the pier frames. The model was validated against test results. Subsequently, a parametric study was conducted with variables such as frame height to span ratio, steel reinforcement ratio, FRP tube thickness, axial force, and compressive strength of concrete. A typical bridge was also simulated under three different ground acceleration records and damping ratios. Based on the analytical damage index, the RCF bridge was most severely damaged, whereas the GFF bridge only suffered minor repairable damages. Damping ratio was shown to have a pronounced effect on FRP-concrete bridges, just the same as in conventional bridges. This research was part of a multi-university project, which is founded by the National Science Foundation (NSF) - Network for Earthquake Engineering Simulation Research (NEESR) program.

Seismic Performance of Hybrid Fiber Reinforced Polymer-Concrete Pier Frame Systems

As an alternative to transverse spiral or hoop steel reinforcement, fiber reinforced polymers (FRPs) were introduced to the construction industry in the 1980's. The concept of concrete-filled FRP tube (CFFT) has raised great interest amongst researchers in the last decade. FRP tube can act as a pour form, protective jacket, and shear and flexural reinforcement for concrete. However, seismic performance of CFFT bridge substructure has not yet been fully investigated. Experimental work in this study included four two-column bent tests, several component tests and coupon tests. Four 1/6-scale bridge pier frames, consisting of a control reinforced concrete frame (RCF), glass FRP-concrete frame (GFF), carbon FRP-concrete frame (CFF), and hybrid glass/carbon FRP-concrete frame (HFF) were tested under reverse cyclic lateral loading with constant axial loads. Specimen GFF did not show any sign of cracking at a drift ratio as high as 15% with considerable loading capacity, whereas Specimen CFF showed that lowest ductility with similar load capacity as in Specimen GFF. FRP-concrete columns and pier cap beams were then cut from the pier frame specimens, and were tested again in three point flexure under monotonic loading with no axial load. The tests indicated that bonding between FRP and concrete and yielding of steel both affect the flexural strength and ductility of the components. The coupon tests were carried out to establish the tensile strength and elastic modulus of each FRP tube and the FRP mold for the pier cap beam in the two principle directions of loading. A nonlinear analytical model was developed to predict the load-deflection responses of the pier frames. The model was validated against test results. Subsequently, a parametric study was conducted with variables such as frame height to span ratio, steel reinforcement ratio, FRP tube thickness, axial force, and compressive strength of concrete. A typical bridge was also simulated under three different ground acceleration records and damping ratios. Based on the analytical damage index, the RCF bridge was most severely damaged, whereas the GFF bridge only suffered minor repairable damages. Damping ratio was shown to have a pronounced effect on FRP-concrete bridges, just the same as in conventional bridges. This research was part of a multi-university project, which is founded by the National Science Foundation (NSF) Network for Earthquake Engineering Simulation Research (NEESR) program.