A brief survey of existing stochastic dynamics methods from the view point of probability of failure estimation in the low probability region(10~8 < P <10~-3) is presented. A selective Monte Carlo simulation technique, namely, Russian Roulette and Splitting technique is applied for the reliability assessment of structures under stochastic excitations. The basic features of the algorithm are described and discussed. As a numerical example the technique is used for the numerical solution of the first passage problem. Results are compared with available solutions, obtained by another variance reduction technique---Double & Clump Procedure.
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