Life behavior of δδ-shock model

Two traditional assumptions in shock models are that the failure of a system is related either to the cumulative effect of a large number of shocks or to the maximum magnitude of shocks ever occur. The present paper provide another type (only concentrating on inter-arrivals) of shock model (called δδ-shock model). For the case with underlying homogeneous Poisson process, some results are given, such as, analytic survival function, moment of any order, class properties and asymptotic behavior of the normalized lifetime TM/E[TM]TM/E[TM] of a system as δ→0δ→0. For another case with underlying non-homogeneous Poisson process with periodic intensity λ(t)λ(t), analytic survival function is given as well. Moreover, under practical conditions, moment of any order is proved to be finite, and asymptotic behavior of T0/E[T0]T0/E[T0] is obtained as δ→0δ→0. This δδ shock model has diverse range of applications.