Abstract. A redundant system with the structure determined by fault tree with efficiency is considered. An external load on the system is a function of the state of a semi-Markov process. A fast simulation method enabling to evaluate the probability of functional failure when the real system efficiency becomes less than required ones is proposed. It is proved that under some weak conditions an estimate has a bounded relative error as the components reliability increases. The numerical example illustrates the efficiency of the method proposed.

Keywords: fault tree with efficiencies, semi-Markov process, functional failure, minimum sections, importance sampling technique, estimate variance, relative mean square error.