On the hazard rate and reversed hazard rate orderings in two-component series systems with active redundancies

The lifetimes of two-component series systems with two active redundancies are compared using the hazard rate and the reversed hazard rate orders. We study the problem of where to allocate the spares in a system to obtain the best configuration. We compare redundancy at component level vs. system level using the likelihood ratio order. For this problem we find conditions under which there is no hazard rate ordering between the lifetimes of the systems.