a generalized δ-shock model in the discrete-time framework

According to the δ-shock model‎, ‎a system subjected to random shocks fails when the inter-arrival time between two successive shocks is less than a critical threshold δ‎. ‎several generalizations of the δ-shock model have been proposed to study shock-exposed systems in different scenarios‎. ‎in this paper‎, ‎we examine a recently proposed generalization of the δ-shock model within a discrete-time framework‎, ‎where inter-arrival times follow a geometric distribution‎. ‎we derive the probability generating function‎, ‎the mean time to failure‎, ‎and the variance of the system lifetime‎. ‎furthermore‎, we present ‎an illustrative example related to crop insurance is presented to demonstrate the practical relevance and applicability of the proposed discrete-time model.