Allocation Policies of Redundancies in Two-Parallel-Series and Two-Series-Parallel Systems

In this paper, comparisons of allocation policies of components in two-parallel-series systems with two types of components are provided with respect to both hazard rate and reversed hazard rate orders. The main results indicate that the lifetime of these kinds of system is stochastically maximized by unbalancing the two classes of components as much as possible. We only assume that the two distributions implied in the model have proportional hazard rates. The same type of comparisons are also given for the dual model, the two-series-parallel systems, but assuming that the distributions implied in the model have proportional reversed hazard rates, and therefore the final conclusion is the opposite; that is, the reliability of the system improves as the similarity between the two parallel subsystems increases.