Reliability optimization of a series-parallel k-out-of-n system with failure ratedepends on working system components

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.