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Reliability assessment is an important issue in reliability engineering. Classical reliability-estimating methods are based on precise (also called “crisp”) lifetime data. It is usually assumed that the observed lifetime data take precise real numbers. Due to the lack, inaccuracy, and fluctuation of data, some collected lifetime data may be in the form of fuzzy values. Therefore, it is necessary to characterize estimation methods along a continuum that ranges from crisp to fuzzy. Bayesian methods have proved to be very useful for small data samples. There is limited literature on Bayesian reliability estimation based on fuzzy reliability data. Most reported studies in this area deal with single-parameter lifetime distributions. This article, however, proposes a new method for determining the membership functions of parameter estimates and the reliability functions of multi-parameter lifetime distributions. Also, a preventive maintenance policy is formulated using a fuzzy reliability framework. An artificial neural network is used for parameter estimation, reliability prediction, and evaluation of the expected maintenance cost. A genetic algorithm is used to find the boundary values for the membership function of the estimate of interest at any cut level. The long-run fuzzy expected replacement cost per unit time is calculated under different preventive maintenance policies, and the optimal preventive replacement interval is determined using the fuzzy decision making (ordering) methods. The effectiveness of the proposed method is illustrated using the two-parameter Weibull distribution. Finally, a preventive maintenance strategy for a power generator is presented to illustrate the proposed models and algorithms. [ABSTRACT FROM AUTHOR]

When solving multi-objective optimization problems subject to constraints in reliability-based design, it is desirable for the decision maker to have a sufficient number of solutions available for selection. However, many existing approaches either combine multiple objectives into a single objective or treat the objectives as penalties. This results in fewer optimal solutions than would be provided by a multi-objective approach. For such cases, a niched Pareto Genetic Algorithm (GA) may be a viable alternative. Unfortunately, it is often difficult to set penalty parameters that are required in these algorithms. In this paper, a multi-objective optimization algorithm is proposed that combines a niched Pareto GA with a constraint handling method that does not need penalty parameters. The proposed algorithm is based on Pareto tournament and equivalence sharing, and involves the following components: search for feasible solutions, selection of non-dominated solutions and maintenance of diversified solutions. It deals with multiple objectives by incorporating the concept of Pareto dominance in its selection operator while applying a niching pressure to spread the population along the Pareto frontier. To demonstrate the performance of the proposed algorithm, a test problem is presented and the solution distributions in three different generations of the algorithm are illustrated. The optimal solutions obtained with the proposed algorithm for a practical reliability problem are compared with those obtained by a single-objective optimization method, a multi-objective GA method, and a hybrid GA method. [ABSTRACT FROM AUTHOR]