Intuitively, activating the standby of a k-out-of-n:G system to the working state at the last moment fully utilizes the redundancy and hence would result in a more reliable system; however, this is not always true as shown in a counterexample. This paper presents several scenarios under which,...

In this paper, we compare the largest order statistics arising from independent heterogeneous gamma random variables based on the likelihood ratio order. Let X1,…,Xn be independent gamma random variables with Xi having shape parameter r∈(0,1] and scale parameter λi, i=1,…,n, and let Xn:n...

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...