A new discrete-time mixed δ-shock model

In this paper, a mixed δ-shock model with discrete-time is studied by combining δshock and extreme shock models. In this model, a system fails in two ways: first, when k interarrival times between two consecutive shocks with magnitude larger than the critical threshold γ are in [δ1,δ2],δ1 δ2; and second, when the interarrival time between two consecutive shocks is less than δ1. The lifetime of the system under the proposed mixed δ-shock model is investigated. Finaly, a numerical example is presented.