Reliability optimization of a k-out-of-n series-parallel system with warm standby components

In this research, a new hybrid model for the redundancy allocation problem (RAP) in a series-parallel configuration with the k-out-of-n subsystem is presented. In the given model, the redundancy policy is set to an active, warm standby, or no redundancy. In warm standby policy, an imperfect switch detected the component's failure and replaced the fail component with a new standby one. So, the subsystems' redundancy policy is one of the model's decision variables. We presented a new objective function for the RAP to calculate the reliability of a system that consists of active and warm standby subsystems. The presented model aims to determine the subsystems' redundancy policy, the type and number of redundant components to maximize the system's reliability, under the system's cost, volume, and weight constraints. To solve the proposed model, we used two Genetic Algorithm (GA) and hybrid GA (HGA) meta-heuristic algorithm with local search. Since the %RPD of HGA is 2.1% (on average) better than GA in solving ten large-scale instances, the result shows the superiority of HGA in comparison with GA for solving the presented RAP.