Birnbaum importance in solving component assignment problems

As an important type of reliability optimization problems, the component assignment problem (CAP) is to find the optimal arrangement of n available components to n positions of a system such that the resulting system reliability is maximized. The CAP is a combinatorial problem in nature and needs effective solution methods. The importance measures of components, e.g., the Birnbaum importance (BI), evaluate the relative strength of a component to system reliability, and can be used in aid to tackle the CAP. This paper studies the competence of the BI in solving the CAP. It proposes some BI-based heuristic methods for the CAP, and evaluates and compares the BI-based heuristics, including the new ones and the existing ones, through comprehensive numerical experiments. It is demonstrated that the heuristics using the BI can solve the CAP satisfactorily and the new heuristics are superior to the existing ones under some situations. Through the analysis to the computational results, this paper suggests a two-phase procedure for solving the CAP, and each phase uses different BI-based heuristics.