On partial orderings between coherent systems with different structures (Q2731310)

Let \({\mathbf X}= (X_1,\dots, X_n)\) and \({\mathbf Y}= \{Y_1,\dots, Y_m)\) be the lifetimes of two sets of independent components and let \(h_1\) and \(h_2\) be reliability structures of two coherent systems such that \(h_1(p_1,\dots, p_n)\leq h_2(p_1,\dots, p_m)\) for all \(p_1,\dots, p_{\max(n,m)}\). If \(X_i\leq_{\text{st}} Y_i\) for all \(i= 1,\dots,\min(n,m)\), then \(h_1({\mathbf X})\leq_{\text{st}} h_2({\mathbf Y})\) (Theorem 3.1). Analogous theorems as for the stochastic ordering are given for failure rate, reversed failure rate and likelihood ratio ordering.