Reliability-redundancy allocation problem considering imperfect fault coverage

The reliability-redundancy allocation problem (RRAP) has been widely investigated during the last decade. In most of existing studies, component failures are assumed to be covered perfectly which means all faults can be timely detected, located, and isolated. However, the coverage could be imperfect in reality and a not-covered component failure may lead to system failure without constraint. In this paper, the RRAP is solved considering the imperfect fault coverage model (IFCM, only faulty components can be covered) and the irrelevance coverage model (ICM, both faulty and irrelevant components can be covered). It has been proved that an excessive level of redundancy may reduce the system reliability rather than improve it when the fault coverage is imperfect. Therefore, when the IFCM and the ICM are considered in the RRAP, in addition to resource constraints, the coverage model itself also limits the level of redundancy. Three benchmark problems are investigated in this paper. The genetic algorithm is adopted to solve the new mixed integer nonlinear programming problem. The results show that the optimal designs of system in the two coverage models are different from the existing researches that only consider the perfect fault coverage model. The redundant components used in the optimal solution are less than the existing studies. The advantage of the ICM over the IFCM is also verified in this paper.