Moment-independent importance measure of basic random variable and its probability density evolution solution

To analyze the effect of basic variable on failure probability in reliability analysis, a moment-independent importance measure of the basic random variable is proposed, and its properties are analyzed and verified. Based on this work, the importance measure of the basic variable on the failure probability is compared with that on the distribution density of the response. By use of the probability density evolution method, a solution is established to solve two importance measures, which can efficiently avoid the difficulty in solving the importance measures. Some numerical examples and engineering examples are used to demonstrate the proposed importance measure on the failure probability and that on the distribution density of the response. The results show that the proposed importance measure can effectively describe the effect of the basic variable on the failure probability from the distribution density of the basic variable. Additionally, the results show that the established solution on the probability density evolution is efficient for the importance measures.