Line sampling based on markov chain simulation for reliability sensitivity analysis with correlative variables

For the reliability sensitivity (RS) problem with correlative normal variables, a RS analysis method by line sampling is presented on the basis of Markov chain simulation. In the method, the correlative normal variables are first transformed into equivalent independent variables. Then, the line sampling algorithm based on Markov chain simulation is employed to estimate the RS of the failure probability with respect to the distribution parameters of the equivalent independent normal variables. Finally, taking advantage of the relationship between the correlative variables and the independent normal variables, the RS of the failure probability with respect to all distribution parameters of the correlative normal variables can be obtained by the chain rule of derivatives. In order to investigate the convergence and precision of the proposed method, the variance and the variation coefficients of the RS estimation are derived. Since Markov chain is employed to simulate the samples located at the failure region, and these simulated samples are used to obtain the important direction of line sampling and also used as random samples of the line sampling, the proposed method has high efficiency. The results of the examples show the efficiency and the precision of the method.