Consider two renewal processes: Nx = {Nx(t ), t ≥ 0} and Ny = {Ny (t ), t ≥ 0}

whose interarrival distributions are discrete with, respective, hazard rate functions

λx (i) and λy (i). For any set of points A, let Nx(A) and Ny(A) denote, respectively, the numbers of renewals that occur at time points in A for the two processes. If λx (i) ≤ λy (i) for all i and either λx (i) or λy (i) is decreasing, show that Nx(A) ≤st Ny(A) for any A.