Stochastic comparisons of parallel and series systems with heterogeneous Birnbaum–Saunders components

In this paper, we discuss stochastic comparisons of lifetimes of parallel and series systems with independent heterogeneous Birnbaum–Saunders components with respect to the usual stochastic order based on vector majorization of parameters. Specifically, let X1,…,Xn be independent random variables with Xi∼BS(αi,βi),i=1,…,n, and X1∗,…,Xn∗ be another set of independent random variables with Xi∗∼BS(αi∗,βi∗),i=1,…,n. Then, we first show that when …