A note on comparisons of k-out-of-n systems with respect to the hazard and reversed hazard rate orders

Let tau(k\n) denote the lifetime of a k-out-of-n system constructed by using n components with independent (not necessarily identically distributed) lifetimes. It is shown that tau(k\n) is Smaller than 7(k-1\n-1) in the hazard rate order for any k and that tau(k\n-1) is smaller than tau(k\n) in the reversed hazard rate order for any k. We thus strengthen and complement some results in Boland et al. [2] and Block et al. [1].