قاسم چراغ

Nowadays, with technological advances and the need for high reliable systems, extensive research has been done in the eld of reliability optimization. Redundancy allocation problem (RAP) is one of the main issues that has been raised in relation to this subject. Many studies have been carried out in this area and many solutions such as redundancy allocations and component failure rate reduction have been brought up to increase the system reliability. In this paper we considered a seriesparallel system with k-out-of-n subsystems and developed a RAP with components failure rate that depend on the number of working components. In this type of failure rate, when a component fails, the remained components work with more pressure and failure rate of these components increases. The system redundancy strategies are considered as cold standby or active for the subsystems. This model has two objective functions (1) maximizing system reliability and (2) minimizing the system cost. The goals of this model are to select the redundancy strategy between active and cold standby and to determine component type and number of allocated redundant components to each subsystem. As RAP belongs to NP-hard problems, so it is very dicult to optimally solve such a problem by using traditional optimization tools. Therefore for solving the model, two eective meta-heuristic algorithms named Non-dominated Sorting Genetic Algorithm (NSGAII) and Non-dominated Ranked Genetic Algorithm (NRGA) are presented. We use design of experiment (DOE) for parameter tuning of this algorithms response surface methodology (RSM) is applied for determining the optimum amount of parameters. Then to illustrate the eectiveness of algorithms, a numerical example is presented and algorithms are compared using ve dierent performance metrics. In order to determine whether there is a signicant dierence between the performance of algorithms, a single factor ANOVA in signicant level ( = 0:05) is performed. Finally performance of the algorithms is analyzed and the results are reported.

This paper presents a mathematical model for a redundancy allocation problem (RAP) for the series-parallel system with k-out-of-n subsystems and failure rate depends on working components of system. It means that failure rate of components increases when a component fails. The subsystems may use either active or cold-standby redundancy strategies, which considered as a decision variable for individual subsystems. Thus, the proposed model and solution methods are to select the best redundancy strategy among active or cold-standby, component type, and levels of redundancy for each subsystem. The objective function is to maximize the system reliability under cost and weight constraints. To solve the model, since RAP belongs to Np-Hard class of the problems, one effective meta-heuristic algorithm named genetic algorithm (GA)is proposed. Then, response surface methodology is applied for algorithm parameter tuning.Finally, we consider the results of solving presented model with a numerical example.