Order statistics, Stochastic orders, System analysis, Asymptotic theory
We formulate a theory that allows us to formulate a simple criterion that ensures that two k-out-of-n systems A and 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 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→0 and as t→∞) of the constituent survival probabilities. We include examples.
Torrado, Nuria and Veerman, J. J. P., "Asymptotic Reliability Rheory of k-out-of-n Systems" (2012). Mathematics and Statistics Faculty Publications and Presentations. 154.