To fast evaluate the small probability that starts from the all-components-up state, the system hits the failed sets before returning to the all-components-up state, Important Sampling or Important Splitting is used commonly. In this paper, a new approach distinguished from Important Sampling and Important Splitting is presented to estimate this small probability of highly dependable Markov system. This new approach achieves variance reduction through improving the estimator itself. The new estimator is derived from the integral equation describing the state transitions of Markov system. That the variance of this estimator is less than that of naive simulation at all time is proved theoretically. Two example involved reliability models with deferred repair are used to compare the methods of RB, IGBS, SB-RBS, naive simulation, and the method presented in this paper. Results show our method has the least RE.
