Characterization of MRL order of fail-safe systems with heterogeneous exponential components

Let X1,…,Xn be independent exponential random variables with Xi having hazard rate λi, i=1,…,n, and Y1,…,Yn be another independent random sample from an exponential distribution with common hazard rate λ. The purpose of this paper is to examine the mean residual life order between the second order statistics X2:n and Y2:n from these two sets of variables. It is proved that X2:n is larger than Y2:n in terms of the mean residual life order if and …