A rare-event estimation of heterogeneous degradation process

We study the special reliability model where preventive repair is used to prevent an instantaneous failure. The dynamic of the system is expressed in terms of the heterogeneous degradation process with successive stages, which are independent but not identically distributed. The calculating of the performance characteristics of such a systems is an important and typically challenging problem. In this paper, we focus on estimating the rare-event failure probability which is usually not analytically available. In order to evaluate the target measure, we apply a variance reduction technique using a special variant of conditional Monte Carlo approach proposed by Asmussen and Kroese in [1]. The relative error of the proposed method is studied numerically. A few numerical results are presented to justify that proposed technique provides comparatively good properties of the relative error when the failure probability become small.