MONTE CARLO SIMULATION OF MULTIVARIATE DISTRIBUTION AND ITS APPLICATION TO STRUCTURAL RELIABILITY ANALYSIS

The reliability analysis of complex limit state functions involving random variables represented by joint probability distributions cannot be evaluated by direct integration. This paper aims to propose a Monte Carlo simulation based on the method for simulating the joint probability functions and estimating the probability of failure of complex limit state functions. A flow chart of probability of failure based on Monte Carlo simulation is presented. Two examples are presented to demonstrate the validity and capability of the proposed methods. The results indicate that the proposed Monte Carlo simulation can produce sufficiently accurate results, especially it is suitable for the reliability problems with complex limit state functions. Both the approximate method P and the approximate method S can lead to the results with a sufficient accuracy. The difference in probabilities of failure between the two approximate methods and the exact method increases with decreasing probability of failure. It increases as the correlation between variables becomes stronger. Significant errors associated with the two approximate methods could be observed when the probability of failure is below 10^-3.