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Multistate reliability has received significant attention over the past decades, particularly its application to mechanical devices that degrade over time. This degradation can be represented by a multistate continuous-time stochastic process. This article considers a device with discrete multistate degradation, which is monitored by a condition monitoring indicator through an observation process. A general stochastic process called the nonhomogeneous continuous-time hidden semi-Markov process is employed to model the degradation and observation processes associated with this type of device. Then, supervised parametric and nonparametric estimation methods are developed to estimate the maximum likelihood estimators of the main characteristics of the model. Finally, the correctness and empirical consistency of the estimators are evaluated using a simulation-based numerical experiment. [ABSTRACT FROM PUBLISHER]

In many industrial environments, maintenance is performed during successive mission breaks. In these conditions, it may not be feasible to perform all possible maintenance actions due to limited maintenance resources such as time, budget, repairman availability, etc. A subset of maintenance actions is then performed on selected components such that the system is able to meet the next mission requirement. Such a maintenance policy is calledselective maintenance. In this article, a selective maintenance strategy is developed for a MultiState System (MSS). The system can have several finite levels of performance in an MSS. Previous studies on selective maintenance have solely focused on MSSs with binary components. However, components in an MSS may be in more than two possible states. Hence, a series-parallel MSS that consists of multistate components is considered in this article. Imperfect maintenance of a component is considered to be a maintenance option, along with the replacement and the do-nothing options. Maintenance resources need to be allocated such that maximum system reliability during the next mission is ensured. A universal generating function is used to determine system reliability. An illustrative example is presented that depicts the advantages of utilizing imperfect maintenance/repair options. [ABSTRACT FROM AUTHOR]

The k-out-of-n system structure is a very popular type of redundancy in fault-tolerant systems, with wide applications in both industrial and military systems. In this paper, the modeling, application and reliability evaluation of k-out-of-n systems are studied for the case where the components and the system have multiple performance levels. A multi-state k-out-of-n system model is proposed that allows different requirements on the number of components for different state levels, and, very importantly, more practical engineering systems can fit into this model. The multiple states in the model can be interpreted in two ways: (i) multiple levels of capacity; and (ii) multiple failure modes. Application examples of the proposed multi-state k-out-of-n system model are given under each of the interpretations. An approach is presented for efficient reliability evaluation of multi-state k-out-of-n systems with identically and independently distributed components. A recursive algorithm is proposed for reliability evaluation of multi-state k-out-of-n systems with independent components. Efficiency investigations show that both of the reliability evaluation approaches are efficient. The multi-state k-out-of-n system model with a constant k value, which is a special case of the general multi-state k-out-of-n system model, has been studied for a long time, but only on the theoretical stage. A practical application of this model is presented in this paper as well. [ABSTRACT FROM AUTHOR]

The multistate networks under consideration consist of a source node, a sink node, and some independent failure-prone components in between the nodes. The components can work at different levels of capacity. For such a network, we are interested in evaluating the probability that the flow from the source node to the sink node is equal to or greater than a demanded flow of d units. A general method for reliability evaluation of such multistate networks is using minimal path (cut) vectors. A minimal path vector to system state d is called a d-MP. Approaches for generating all d-MPs have been reported. Given that all d-MPs have been found, the issue becomes how to evaluate the probability of the union of the events that the component state vector is greater than or equal to at least one of the d-MPs. There is a need for a more efficient method of determining the probability of this union of events. In this paper, we report an efficient recursive algorithm for this union probability evaluation based on the Sum of Disjoint Products (SDP) principle, and name it the Recursive Sum of Disjoint Products (RSDP) algorithm. The basic idea is that, based on the SDP principle and a specially defined "maximum" operator, "⊕", the probability of a union with L vectors can be calculated via calculating the probabilities of several unions with L-1 vectors or less. The correctness of RSDP is illustrated. The efficiency of this algorithm is investigated by comparing it with an existing algorithm that is generally accepted to be efficient. It is found that RSDP is more efficient than the existing algorithm when the number of components of a system is not too small. RSDP provides us with an efficient, systematic and simple approach for evaluating multistate network reliability given all d-MPs. [ABSTRACT FROM AUTHOR]

This article considers the determination of the optimal burn-in time, the degree of preventive maintenance, and the preventive maintenance interval (or, equivalently, the number of preventive maintenance actions) for warranted products with time-dependent maintenance costs. The expected cost function is derived by adopting an appropriate age-reduction model and the determination of the optimal joint solution is discussed. Finally, the impact of providing a burn-in/preventive maintenance program is evaluated through numerical examples. [ABSTRACT FROM PUBLISHER]

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]

In most practical situations involving reliability optimization, there are several mutually conflicting goals such as maximizing the system reliability and minimizing the cost, weight and volume. This paper develops an effective multiobjective optimization method, the Intelligent Interactive Multiobjective Optimization Method (IIMOM). In IIMOM, the general concept of the model parameter vector is proposed. From a practical point of view, a designer's preference structure model is built using Artificial Neural Networks (ANNs) with the model parameter vector as the input and the preference information articulated by the designer over representative samples from the Pareto frontier as the desired output. Then with the ANN model of the designer's preference structure as the objective, an optimization problem is solved to search for improved solutions and guide the interactive optimization process intelligently. IIMOM is applied to the reliability optimization problem of a multi-stage mixed system with five different value functions simulating the designer in the solution evaluation process. The results illustrate that IIMOM is effective in capturing different kinds of preference structures of the designer, and it provides a complete and effective solution for medium- and small-scale multiobjective optimization problems. [ABSTRACT FROM AUTHOR]

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]