Tail behaviour of consecutive 2-within-m-out-of-n systems with nonidentical components

We study the asymptotic behaviour of the hazard rate function of consecutive k-within-m-out-of-n   systems when k=2k=2. The consecutive k-within-m-out-of-n systems provide a generalization of consecutive k-out-of-n   (m=km=k) and k-out-of-n   (m=nm=n) systems which have been used to model different engineering systems. Here, we consider the case of independent nonidentically distributed component lifetimes. In addition, we obtain some stochastic properties for consecutive 2-within-m-out-of-n systems consisting of components satisfying the proportional hazard rate model.