Consider a system exposed to random shocks over time. Many shock models have been proposed in the literature to anticipate future behaviors, assessments, and decisions regarding resilience in the face of unexpected disruptions. Among these, the δ-shock model is a fundamental concept in reliability theory and related disciplines. In this shock model, the system fails if the time interval between two consecutive shocks is shorter than a specified threshold δ. In this paper, we examine a mixed δ-shock model, where the system fails if either the inter-arrival time between two consecutive shocks falls within the interval (δ1,δ2), where δ1≤δ2, or if the shock magnitude exceeds a specified threshold η. We obtain some characteristics of the system’s lifetime distribution under the new shock model and provide some numerical examples. We also correct some of the results of some shock models in the literature.
