Evaluation of the Probability of Functional Failure of a Redundant System by Importance Sampling Method

A redundant system whose structure is determined by the fault tree with efficiencies is considered. External load on the system is the function of 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. The conditions that guarantee the boundedness of the relative error estimate as the reliability of elements increases are found. The numerical example illustrates the the accuracy of estimates obtained by the proposed method.