Shock models leading to G* class of lifetime distributions

In this paper we study a stochastic ordering namely alternate probability generating function (a.p.g.f .... ) ordering and its properties. The life distribution H(t) of a device subject to shocks governed by a Poisson process is considered as a function of the probabilities Pk of surviving the first k shocks. Various properties of the discrete failure distribution Pk are shown to be reflected in corresponding properties of the continuous life distribution H(t). A certain cumulative damage model and various applications of these models in reliability modeling are also considered.