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

An Expectation Maximization Algorithm to Model Failure Times by Continuous-Time Markov Chains

In many applications, the failure rate function may present a bathtub shape curve. In this paper, an expectation maximization algorithm is proposed to construct a suitable continuous-time Markov chain which models the failure time data by the first time reaching the absorbing state. Assume that a system is described by methods of supplementary variables, the device of stage, and so on. Given a data set, the maximum likelihood estimators of the initial distribution and the infinitesimal transition rates of the Markov chain can be obtained by our novel algorithm. Suppose that there are m transient states in the system and that there are n failure time data. The devised algorithm only needs to compute the exponential of m×m upper triangular matrices for O(nm2) times in each iteration. Finally, the algorithm is applied to two real data sets, which indicates the practicality and efficiency of our algorithm

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

Modelamiento de la disponibilidad de una estructura en serie reparable con dos unidades

When there is a structure with two serial components where each one owns a life time that is distributed exponentially and both of the components are repairable, it is established a renovation process, in which both components need to be working in order for the operation of the structure. It is observed that the renovation process evidences a semimarkovian behavior and it is shown that through this one, its availability function is one of the inquiries of a system of integral equations that is solved by a numerical method designed for that purpose. The novelty in this article is that it is considered a process whose state space includes repair time, which is useful in engineering applications.Cuando se tiene una estructura con dos componentes dispuestas en serie y en donde cada una de ellas tiene un tiempo de vida que se distribuye exponencialmente, y además las componentes son reparables, se establece un proceso de renovación, en el cual para que la estructura esté operando se requiere que ambas componentes estén en funcionamiento. Este proceso de renovación tiene un comportamiento semimarkoviano y se demuestra que, a partir de este, su función de disponibilidad es una de las incógnitas de un sistema de ecuaciones integrales, que se resuelve usando un método numérico diseñado para tal fin. Lo novedoso de este articulo es que se considera un proceso cuyo espacio de estados incluye el tiempo de reparación, lo cual es de utilidad en aplicaciones de ingeniería.&nbsp

Reliability Analysis And Optimal Maintenance Planning For Repairable Multi-Component Systems Subject To Dependent Competing Risks

Modern engineering systems generally consist of multiple components that interact in a complex manner. Reliability analysis of multi-component repairable systems plays a critical role for system safety and cost reduction. Establishing reliability models and scheduling optimal maintenance plans for multi-component repairable systems, however, is still a big challenge when considering the dependency of component failures. Existing models commonly make prior assumptions, without statistical verification, as to whether different component failures are independent or not. In this dissertation, data-driven systematic methodologies to characterize component failure dependency of complex systems are proposed. In CHAPTER 2, a parametric reliability model is proposed to capture the statistical dependency among different component failures under partially perfect repair assumption. Based on the proposed model, statistical hypothesis tests are developed to test the dependency of component failures. In CHAPTER 3, two reliability models for multi-component systems with dependent competing risks under imperfect assumptions are proposed, i.e., generalized dependent latent age model and copula-based trend-renewal process model. The generalized dependent latent age model generalizes the partially perfect repair model by involving the extended virtual age concept. And the copula-based trend renewal process model utilizes multiple trend functions to transform the failure times from original time domain to a transformed time domain, in which the repair conditions can be treated as partially perfect. Parameter estimation methods for both models are developed. In CHAPTER 4, based on the generalized dependent latent age model, two periodic inspection-based maintenance polices are developed for a multi-component repairable system subject to dependent competing risks. The first maintenance policy assumes all the components are restored to as good as new once a failure detected, i.e., the whole system is replaced. The second maintenance policy considers the partially perfect repair, i.e., only the failed component can be replaced after detection of failures. Both the maintenance policies are optimized with the aim to minimize the expected average maintenance cost per unit time. The developed methodologies are demonstrated by using applications of real engineering systems

A unified methodology of maintenance management for repairable systems based on optimal stopping theory

This dissertation focuses on the study of maintenance management for repairable systems based on optimal stopping theory. From reliability engineering’s point of view, all systems are subject to deterioration with age and usage. System deterioration can take various forms, including wear, fatigue, fracture, cracking, breaking, corrosion, erosion and instability, any of which may ultimately cause the system to fail to perform its required function. Consequently, controlling system deterioration through maintenance and thus controlling the risk of system failure becomes beneficial or even necessary. Decision makers constantly face two fundamental problems with respect to system maintenance. One is whether or when preventive maintenance should be performed in order to avoid costly failures. The other problem is how to make the choice among different maintenance actions in response to a system failure. The whole purpose of maintenance management is to keep the system in good working condition at a reasonably low cost, thus the tradeoff between cost and condition plays a central role in the study of maintenance management, which demands rigorous optimization. The agenda of this research is to develop a unified methodology for modeling and optimization of maintenance systems. A general modeling framework with six classifying criteria is to be developed to formulate and analyze a wide range of maintenance systems which include many existing models in the literature. A unified optimization procedure is developed based on optimal stopping, semi-martingale, and lambda-maximization techniques to solve these models contained in the framework. A comprehensive model is proposed and solved in this general framework using the developed procedure which incorporates many other models as special cases. Policy comparison and policy optimality are studied to offer further insights. Along the theoretical development, numerical examples are provided to illustrate the applicability of the methodology. The main contribution of this research is that the unified modeling framework and systematic optimization procedure structurize the pool of models and policies, weed out non-optimal policies, and establish a theoretical foundation for further development

Reliability Modeling and Evaluation in Aging Power Systems

Renewal process has been often employed as a mathematical model of the failure and repair cycle of components in power system reliability assessment. This implies that after repair, the component is assumed to be restored to be in as good as new condition in terms of reliability perspective. However, some of the components may enter an aging stage as the system grows older. This thesis describes how aging characteristics of a system may impact the calculation of commonly used quantitative reliability indices such as Loss of Load Expectation (LOLE), Loss of Load Duration (LOLD), and Expected Energy Not Supplied (EENS). To build the history of working and failure states of a system, Stochastic Point Process modeling based on Sequential Monte Carlo simulation is introduced. Power Law Process is modeled as the failure rate function of aging components. Power system reliability analysis can be made at the generation capacity level where transmission constraints may be included. The simulation technique is applied to the Single Area IEEE Reliability Test System (RTS) and the results are evaluated and compared. The results show that reliability indices become increased as the age of the system grows

A maintenance model for the supply-buffer-demand production system

Master'sMASTER OF ENGINEERIN