Optimal Allocation of Multistate Components in Consecutive Sliding Window Systems

This paper considers a system consisting of n linearly ordered multistate components. Each component can have different states: from complete failure, up to perfect functioning. A performance rate is associated with each state. The system fails if in each of at least m consecutive overlapping groups of r consecutive components (windows) the sum of the performance rates of components belonging to the group is lower than a minimum allowable level. It is shown that, in the case of different components, the system reliability depends on their arrangement. The optimal arrangement problem is formulated, and a numerical tool for solving this problem is suggested. The tool uses an extended universal moment generating function technique for system reliability evaluation, and a genetic algorithm for optimization. Examples of system reliability optimization are presented.