Let τk|n denote the lifetime of a k-out-of-n system, where the n components have independent lifetimes Ti with completely arbitrary distribution Fi, i = 1,..., n. It is shown that τk+1|n ≤hr τk|n, τk|n ≤hr τk−1|n−1, and τk|n−1 ≤hr τk|n if Ti ≤hrTn, i = 1,..., n − 1; τk+1|n ≤rh τk|n, τk−1|n ≤rh τk|n, and τk|n ≤rh τk−1|n−1 if Tn ≤rhTi, i = 1,..., n − 1. These results are available in the literature for the special case of Fi's being absolutely continuous. Also, even in this case, the proofs are often tedious and use the concept of “totally positive of order infinity in differences of k.” In contrast, the proofs given here are simple and elegant and do not use the above concept.