Poisson shock models leading to new classes of non-monotonic aging life distributions

Suppose a device is subjected to a sequence of shocks occurring randomly in time according to a homogeneous Poisson process. In this paper we introduce a class of non-monotonic aging distributions, the so-called New Worse then Better than Used in Failure Rate (NWBUFR) and New Worse then Better than Average Failure Rate (NWBAFR). It is shown under appropriate conditions on the probability of surviving a given number of shocks that the non-monotonic aging classes NWBUFR and NWBAFR arise from suitable Poisson shock models.