We compare the hazard rate functions of the largest order statistic arising from independent heterogeneous gamma random variables and that arising from i.i.d. gamma random variables. Specifically, let X1,…,Xn be independent gamma random variables with Xi having shape parameter 0r≤1 and scale...

In this paper, we derive mixture representations for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under the condition that at least j and at most k−1 (jk) components have failed by time t....