A new mixed δ-shock model

Abstract

In this paper, we introduce and study a realistic shock model. In this new type of mixed δ-shock model, it is assumed that the failure of a system subjected to a random sequence of shocks occurs if a shock exceeds a given tolerance level or two strong shocks, not necessarily consecutive, occur in an interval of length δ. We provide the distribution of the number of shocks until the failure of the system. Special attention is given to the Poisson case. A lower bound for the expected index of the fatal shock is also obtained.