Multitype Optimal Component Allocation of Multicomponent Systems Considering Fuzzy State

A real system may go through several states ranging from full performance to complete failure, carrying out infinite partial performances during service time. This article portrays such a nonbinary state of systems via the fuzzy membership function. Then, the relation between the system reliability under the binary state and that under the fuzzy state is deduced, on which a multitype component allocation problem (MCAP) is investigated to search for the optimal permutation of different types of components to maximize the fuzzy system reliability. After that, we inherit the exploration ability of genetic algorithm (GA) and the exploitation ability of Birnbaum importance (BI) to propose a fuzzy-BI-based two-stage approach combined with GA in order to deal with the MCAP under fuzzy state assumption efficiently and accurately. The k-out-of-n systems in both low and high dimensions are presented to illustrate the effectiveness of the proposed algorithm and demonstrate the similarity and difference between the MCAP under binary state and that under fuzzy state. The experimental results showcase that the proposed approach outperforms the existing state-of-the-art approaches for MCAP.