Comparison of order statistics in a random sequence to the same statistics with i.i.d. variables
The paper is motivated by the stochastic comparison of the reliability of non-repairable k-out-of-n systems. The lifetime of such a system with nonidentical components is compared with the lifetime of a system with identical components. Formally the problem is as follows. Let Ui,i = 1,...,n, be positive independent random variables with common distribution F. For λi > 0 and µ > 0, let consider Xi = Ui/λi and Yi = Ui/µ, i = 1,...,n. Remark that this is no more than a change of scale for each...