Reliability sensitivity measure based on reliability sensitivity function and its solution by conditional probability simulation method

In case that distribution parameters of the basic random variables are uniformly distributed interval variables in reliability analysis, the reliability sensitivity is a function of the distribution parameters. The conditional probability Markov chain simulation method is proposed to obtain the reliability sensitivity function and a new sensitivity measure, which is the statistics characteristic value of the reliability sensitivity function in the space of the distribution parameters. The formulas of the reliability sensitivity function and the sensitivity measure for a linear limit state function with normally distributed variables are derived. The proposed method obtains the formulas of the reliability sensitivity function by the Bayes rule, and Markov chain algorithm is adopted to directly simulate the samples of the failure regions. The third order maximum entropy method is implemented to estimate the conditional probability distributional function and finally the reliability sensitivity function is obtained. The accuracy, efficiency and applicability of the proposed method are demonstrated by several examples. The results show that the proposed method can efficiently estimate the reliability sensitivity function with high accuracy. The proposed method should be valuable for reliability-based optimization.