Uniformization and exponential transformation: Techniques for fast simulation of highly dependable non-Markovian systems

The authors consider the estimation of system unreliability in highly dependable non-Markovian systems. They describe two alternative approaches to importance sampling for estimating transient reliability measures in such systems. One is based on the uniformization method of Monte Carlo simulation and the other uses an importance sampling distribution in which the failure times of components are sampled from the exponential distribution with rates higher than the original hazard rates. Implementation issues relevant to estimating system unreliability are discussed. Experimental results are given to illustrate the effectiveness of the proposed importance sampling techniques. Besides several small examples used for experimentation, a large example is used to illustrate the effectiveness of this technique for problems that are analytically intractable.