Aging Properties of a Discrete-Time Failure and Repair Model

We introduce a failure and repair model that is a discrete-time version of the pure birth shock model. Its discrete lifetime is a random sum with support on N, and with geometric summands, that represent the number of successful tasks between consecutive shocks performed by an engineering system. We provide distributional properties and conditions that lead to the discrete aging properties of such random sums. Our results provide qualitative insight into the discrete lifetime distribution of our model.