Estimation of reliability and its derivatives for large time horizons in Markovian systems

A number of importance sampling methods have been previously proposed for estimating the system unreliability of highly reliable Markovian systems. These techniques are effective when the time horizon of interest is small. However, for large time horizons, these methods are no longer efficient. We describe a technique in which instead of estimating the actual measure, we estimate bounds on the measure. The bounds can be estimated efficiently, and for large time horizons, they are close to the actual measure. Similar techniques for derivative estimation are also presented.