a note on a generalization of the δ-shock model

According to the δ-shock model‎, ‎a shock-exposed system fails when an intershock time falls below a critical threshold δ. ‎recently‎, ‎a generalization of the δ-shock model was introduced by poursaeed (2019)‎ ‎under which the system fails when the intershock time falls below a threshold δ1‎>0 ‎and also the system probably fails with probability θ if the intershock time falls in the interval (δ1‎,δ2‎] for ‎δ1‎<δ2. ‎in this paper‎, ‎we look at this generalized model with new assumptions for intershock times‎. ‎more precisely‎, ‎we assume that the intershock times have a discrete distribution‎, ‎and the chance of their occurrence at a critical time point is significantly high‎. ‎we investigate some statistical properties of the system's lifetime‎, ‎and by providing an illustrative example‎, ‎we examine theoretical results numerically‎. ‎numerical results show that when the chance of intershock times occurring at a critical time point increases‎, ‎the system reliability decreases significantly‎. ‎finally‎, ‎the paper ends with a conclusion‎.