Asymptotic reliability theory of k-out-of-n systems

We formulate a theory that allows us to formulate a simple criterion that ensures that two k-out-of-n systems A   and A˜ are not ordered. If the systems fail the criterion, it does not follow they are ordered. Thus the theory only serves to avoid some a priori useless comparisons: when neither A   nor A˜ can be said to be better than the other. The power of the theory lies in its wide potential applicability: the assumptions involve very weak estimates on the asymptotic behavior (as t→0t→0 and as t→∞t→∞) of the constituent survival probabilities. We include examples.