A New Stochastic Model for Systems Under General Repairs

Numerous stochastic models for repairable systems have been developed by assuming different time trends, and re- pair effects. In this paper, a new general repair model based on the repair history is presented. Unlike the existing models, the closed- form solutions of the reliability metrics can be derived analytically by solving a set of differential equations. Consequently, the con- fidence bounds of these metrics can be easily estimated. The pro- posed model, as well as the estimation approach, overcomes the drawbacks of the existing models. The practical use of the proposed model is demonstrated by a much-discussed set of data. Compared to the existing models, the new model is convenient, and provides accurate estimation results

Розрахунок інтенсивності потоку відмов дубльованої системи з паралельним резервуванням

Розглянуто проблему розрахунку інтенсивності потоку відмов для дубльованої відновлюваної системи з паралельним резервуванням. Інтенсивність потоку відмов системи пропонується визначати шляхом застосування спеціального методу, який ґрунтується на марковській моделі на основі розширення простору станів. Коректність такого підходу перевірено методом Монте-Карло.The paper is devoted to problem of failure intensity calculation for doubled repairable system with parallel redundancy. Failure intensity determination is suggested by using special method for extended Markov reliability model. The correctness for such approach is verified by Monte-Carlo method

A general-purpose tool for reliability and availability analysis of repairable systems

Mestrado de dupla diplomação com a UTFPR - Universidade Tecnológica Federal do ParanáThis thesis covers general mathematical and simulation models for the reliability and availability analysis of repairable systems along with estimation methods and model selection criterion. A combined mathematical and simulation model called the Failure-Repair Process is proposed, based on the trend-renewal process. This model is based on a binary state system, where the system may only be in one of two states: working or failed. This model is then integrated into a general-purpose tool, for automated modelling of repairable systems. The classical Akaike information criterion is used to automate the choice of failure and repair models that best fit the available data. Estimators for different performance measures of the systems are studied, such as point and mean availability, rate of occurrence of failures and a first order reliability estimator based on the Kaplan-Meier estimator. Numerical studies are conducted in the proposed non-analytical estimators for the availability, leading to a robust mean availability estimator and a intuitive but sample demanding point availability estimator. Furthermore, a complete quantitative study is conducted on real data from the food industry together with a presentation of the implemented tool functionalities. Overall, the proposed model is able to adapt very well to real data with different characteristics, and, consequently, the resulting performance indicators are befitting to practice.Esta tese aborda modelos matemáticos e de simulação para a análise de confiabilidade e disponibilidade de sistemas reparáveis, juntamente com métodos de estimação e critério de seleção de modelos. Um modelo matemático e de simulação combinados denominado Failure-Repair Process é proposto, baseado no trend-renewal process. Este modelo consiste em um sistema de caracterização binária, onde o sistema pode estar em apenas um de dois estados: em funcionamento ou falha. Este modelo é então integrado em uma ferramenta de uso geral, para modelagem automatizada de sistemas reparáveis. O clássico critério de informação de Akaike é usado para automatizar a escolha dos modelos de falha e reparo que melhor se ajustam aos dados disponíveis. São estudados estimadores para diferentes medidas de desempenho dos sistemas, tais como disponibilidade pontual e média, taxa de ocorrência de falhas e um estimador de confiabilidade de primeira ordem baseado no estimador Kaplan-Meier. Estudos numéricos são conduzidos nos estimadores nãoanalíticos propostos para a disponibilidade, levando a um estimador de disponibilidade média robusto e um estimador de disponibilidade puntual intuitivo, mas que demanda grandes amostras. Além disso, é realizado um estudo quantitativo completo sobre dados reais da indústria de alimentos juntamente com uma apresentação das funcionalidades da ferramenta implementada. De maneira geral, o modelo proposto é capaz de se adaptar muito bem a dados reais com diferentes características e, consequentemente, os indicadores de desempenho resultantes são adequados à prática

A case study in estimating avionics availability from field reliability data

Under incentivized contractual mechanisms such as availability-based contracts the support service provider and its customer must share a common understanding of equipment reliability baselines. Emphasis is typically placed on the Information Technology-related solutions for capturing, processing and sharing vast amounts of data. In the case of repairable fielded items scant attention is paid to the pitfalls within the modelling assumptions that are often endorsed uncritically, and seldom made explicit during field reliability data analysis. This paper presents a case study in which good practices in reliability data analysis are identified and applied to real-world data with the aim of supporting the effective execution of a defence avionics availability-based contract. The work provides practical guidance on how to make a reasoned choice between available models and methods based on the intelligent exploration of the data available in practical industrial applications

A critical look at some point process models for repairable systems

The use of a modeldriven approach to the analysis of repairable systems is considered and shown to be useful as a way of understanding the characteristics of such a system. However, considerable statistical problems arise from the use of a set of standard model-building elements. In particular, identification problems arise in many of the models. The argument is illustrated by examples from software reliability and mechanical reliability. The conclusion is that, in many cases, the exploratory data-analysis approach is as effective as the use of more sophisticated models

Semi-parametric evaluation of rapid rate-of-change proportional intensity models for repairable systems with censoring.

Keywords. repairable systems reliability, right-censoring, recurrent events, proportional intensity models, log-linear intensity functionThis research investigates the robustness of four leading proportional intensity (PI) models: PWP-gap time (PWP-GT), PWP-total time (PWP-TT), Andersen-Gill (AG), and Wei-Lin-Weissfeld (WLW), for right-censored recurrent failure event data that follow a Non-homogeneous Poisson Process (NHPP) with log-linear constant or increasing intensity function. The results are beneficial to practitioners in anticipating the more favorable applications domains and selecting appropriate PI models for monitoring failure trends and for decisions in preventive maintenance, service parts inventory, and repair versus replacement. The experimental design has incorporated four levels of censoring severity, three levels of sample size, and seven levels of shape parameter to evaluate these four proposed PI models. The effect of failure event count is also studied. The models of choice are the PWP-GT (for increasing rate of occurrence of failures and low event count) and AG (for constant rate of occurrence of failures), evaluated in terms of three robustness metrics: bias, mean absolute deviation, and mean squared error of covariate regression coefficients. The more favorable engineering application ranges are recommended. Robustness of the PWP-GT for the case of an underlying log-linear increasing intensity function tends to be sensitive to the failure event count. For lower failure counts (N ≤ 4), the PWP-GT proves to perform well for moderate to severe right-censoring (40% to 80% of units censored), constant and moderately increasing rates of occurrence of failure (log-linear NHPP shape parameter in the range of 0 ≤ theta ≤ 0.01), and small to large sample size (60 ≤ U ≤ 180). The AG model proves to outperform the PWP-TT and WLW for stationary process (HPP) across a wide range of right censorship (0% to 100%) and for sample size of 60 or more. A highly automated SAS macro proved to be a valuable tool for the research infrastructure in this and future studies

Random Effect Models For Repairable System Reliability

The practical motivation for the work described in this thesis arose from the development of a new Jaguar car engine. Development tests on prototype engines led to multiple failure time data which are modelled as a non-homogeneous Poisson process in its log-linear form. Initial analysis of the data using failure time plots showed considerable differences between prototype engines and suggested the use of models incorporating random effects for the engine effects. These models were fitted using the method of maximum likelihood. Two random effects have been considered: a proportional effect and a time dependent effect. In each case a simulation study showed the method of maximum likelihood to produce good estimates of the parameters and standard errors. There is also shown to be a bias in the estimate of the random effect, especially in smaller samples. The likelihood ratio test has been shown to be valid in assessing the statistical significance of the random effect, and a simulation exercise has demonstrated this in practical terms. Applying this test to the models fitted to the Jaguar data gives the proportional random effect to be significant while the time dependent random effect is not found to be significantly different from zero. This test has also been demonstrated to be of use in distinguishing between the two models and again the proportional random effect model is found to be more suitable for the Jaguar data. Residual analysis is performed to aid model validation Covariates are included, in various forms, in the proportional random effect model and the inclusion of these in the time dependent model is briefly discussed. The use of these models is demonstrated for the Jaguar data by including the type of test an engine performed as a covariate. The covariate models have also been used to compare engine phases. A framework for extending the models for interval censored data is developed. Finally this thesis discusses possible extensions of the work summarised in the previous paragraphs. This includes work on alternative models, Bayesian methods and experimental design.Jaguar Cars Limite