Accelerated simulation of the failure probability of a system on the busy period for nonexponential distributions defining the processes of failure and restoration of elements (Q1974316)

The new methods of accelerated simulation of the time to the failure distribution demand that the estimate of the variance is less than that in the traditional simulation. It is a rule that for an unbiased estimate \((E\widehat q=q)\), the boundedness of the relative root mean square error \(\sqrt{E\widehat q^2/q^2- 1}\) assures an accuracy of the estimate. The paper describes an algorithm for estimating the probability that the failure of a non-Markovian, renewal system will occurs on the busy period. The algorithm, to complicate to be presented here in details, is based on the so-called importance sampling technique.