On some general survival models with delayed failures

In practice, the point events (e.g., shocks) affecting a system often result in some consequences only after some random delays. In this paper, we generalize the previous results reported in the literature to a meaningful case of the generalized Polya process of initial shocks, which is characterized by dependent increments. We derive and analyze the distribution of the lifetime and the failure rate of a system. Generalizations to the cases when each initial shock triggers the delay only with a given probability and when it results in the corresponding wear process are also considered.