On Conditional Monte Carlo for the Failure Probability Estimation

We consider the system with gradual and instantaneous failures described in terms of the so-called degradation process composed by a sum of the successive phases, where preventive repair is used to prevent an instantaneous failure. The calculating the failure probability is an important and hard problem, arising in the optimal control of such a systems. The required performance measure is usually not analytically available. Thus, one has to rely on simulation technique. We develop a variance reduction technique to estimate the target failure probability using a conditional Monte Carlo method is based on the algorithm proposed by Asmussen and Kroese in [1]. The effectiveness of the proposed approach is investigated through simulations in terms of relative error. We present a few numerical results which indicate that proposed approach provides comparatively accurate results.