Algorithm for Solving the Component Assignment Problem in a Multistate Sliding Window System

The multistate sliding window system (SWS) comprises n multistate components arranged in a line; each group of r consecutive multistate components is considered as a window. If the total performance rate in a window does not meet the predetermined demand W, then that window is regarded as a failure. The SWS fails if and only if there exists at least one failed window. Several researchers have considered the component assignment problem for the SWS with the aim of finding an appropriate component arrangement that maximizes system reliability. Such an arrangement is called the optimal arrangement. Although several metaheuristic and heuristic algorithms have been proposed, an exact algorithm for solving the component assignment problem of the SWS has not been developed thus far. Therefore, in this study, a branch-and-boundbased algorithm is developed to determine the optimal arrangement of the SWS efficiently. Furthermore, a recursive method is proposed to compute the system reliability. Combining the branch-and-bound-based algorithm with the recursive method enables reduction of the complexity of the reliability computations for determining the optimal arrangement. To investigate the efficiency of the branch-and- bound- based algorithm, numerical experiments were conducted; it was observed that the parameters n and r have the maximum effect on computation time, whereas parameter W has minimal effect. The proposed algorithm is useful for improving the reliability of a practical system that can be expressed as an SWS. In addition, the optimal arrangements can be used to measure the heuristic and metaheuristic performances because they guarantee global optimality.