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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 $U_i,i=1,...,n,$ be positive independent random variables with common distribution $F$. For ${\lambda }_i\>0$ and $\mu \>0$, let consider $X_i=U_i/{\lambda }_i$ and $Y_i=U_i/\mu ,i=1,...,n$. Remark that this is no more than a change of scale for each term. For $k\in \{1,2,...,n\},$ let us define $X_{k:n}$ to be the $k$th order statistics...

The paper is motivated by the stochastic comparison of the reliability of non-repairable -out-of- 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 be positive independent random variables with common distribution . For λ > 0 and µ > 0, let consider and . Remark that this is no more than a change of scale for each term. For , let us define to be the th order...