Birnbaum importance-based simulated annealing algorithm for solving the component assignment problem of linear connected-(r, s)-out-of-(m, n):F lattice systems

The component assignment problem (CAP) is one of the most important problems in reliability engineering. This paper proposes a Birnbaum importance-based simulated annealing (SA) algorithm for the CAP of linear connected-(r, s)-out-of-(m, n):F lattice systems. Here, the CAP is assigning the components to maximize system reliability, and Birnbaum importance is a measure of the importance of a component assigned at a certain position in the CAP. If the number of components is small, this problem can be solved within an acceptable time by enumerating all solution candidates. However, it is difficult to solve the problem by using this approach with large numbers of components, because the required computational time increases rapidly with the number of components. Based on these factors, we propose an algorithm to solve the CAP of large-sized linear connected-(r, s)-out-of-(m, n):F lattice systems within an acceptable time. We performed numerical experiments to evaluate the effectiveness of combining Birnbaum importance and SA because the proposed algorithm could aid in designing reliable systems.