A Universal Generating Function Approach for Redundancy Optimization for Hot-Standby Multi-State Series Parallel k-out-of-n Systems

An effective method to provide the required level of reliability and availability is Components redundancy. In this paper redundancy allocation of multi-state series-parallel system is considered which in each of the subsystems at least k-out-of-n components must be working properly since the whole system continues it´s working. The goal is finding the optimum combination which satisfies required reliability of the system with the minimum cost. Thus the number of component in each subsystems and the number of stand-by components must be found. Since this problem is non-convex which is difficult to solve by traditional optimization techniques, Universal Generation Function (UGF) technique and Genetic Algorithm (GA) is employed to solve the problem. Finally a case study is considered to illustrate the efficiency of the proposed approach.