Reliability and Cost Optimization of a System with k-out-of-n Configuration and Choice of Decreasing the Components Failure Rates

Document Type: Article


1 Department of Industrial Engineering, Islamic Azad University, Qazvin Branch

2 Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, QIAU

3 Faculty of Industrial Engineering, Amirkabir University of Technology

4 Management Department, Islamic Azad University, South Tehran Branch, Iran



This paper presents a new redundancy allocation problem for a system with the k-out-of-n configuration at the subsystems’ level with two active and cold standby redundancy strategies. The failure rate of components in each subsystem depends on the number of working components. The components are non-reparable, and the failure rate of the component can be decreased with some preventive maintenance actions. The model has two objective functions: maximizing the system’s reliability and minimizing the system’s costs. The system aims to find the type and number of components in each subsystem, redundancy strategy of subsystems, as well as the decreased values of components failure rates in subsystems. Since the redundancy allocation problem belongs to NP-Hard problems, two Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Non-Dominated Ranked genetic algorithm (NRGA) metaheuristic algorithms were used to solve the presented model and to tune algorithms parameters we used response surface methodology (RSM). Besides, these algorithms were compared using five different performance metrics. Finally, the hypothesis test was used to analyze the results of the algorithms.