Reliability optimization of k-out-of-n system with random selection of allocative components

This paper studies the optimal component allocation policy of a k-out-of-n system composed of n independent subsystems. Each subsystem includes one or several allocative components arranged in parallel [series], and these allocative components are drawn from a randomly selected batch of manufactured components. We compare two allocation policies by means of the majorization order. As a consequence, we get the optimal allocation policy under the constraint of the maximum number of components allowed for each subsystem and the entire system. We also analyze the influence of the batches heterogeneity on the k-out-of-n system reliability. Finally, several illustrative examples are presented.