In Chap. 8, a new point process, the Generalized Polya Process (GPP), has been characterized and its simple reliability application has been discussed. The crucial distinction of the GPP from the nonhomogeneous Poisson process (NHPP) is that the former does not possess the property of independent increments, which is really appealing as many real world problems can be described via the dependent events. For instance, in various shock models, a system’s susceptibility to shocks increases with the number of shocks experienced previously and the GPP models this phenomenon. As another example, the future reliability performance of a system deteriorates faster as the number of system failures in the past increases.