Moment-independent importance measure of basic variable and its state dependent parameter solution

► Two new moment-independent importance measures of the input variable are proposed. ► The intrinsic relationship of two proposed importance measures with the variance-based importance measures is revealed. ► The high-efficient SDP solutions for two importance measures are established. To analyze the effect of basic variable on output of the structure or system in reliability engineering, two moment-independent importance measures of the basic variable are proposed respectively on the failure probability and distribution function of the output. The importance measures proposed not only inherit the advantages of the traditional moment-independent importance measures, but also reflect the intrinsic relationship of the moment-independent measures and the corresponding variance-based importance measures. For the problem that the computational effort of the moment-independent importance measure is usually too high, the computation of the proposed moment-independent importance measures is transformed into that of the variance-based importance measures on their intrinsic relationship. And then combining the high efficient state dependent parameter (SDP) method for the calculation of the conditional moments of the model output, a SDP solution is established to solve two moment-independent importance measures. Several examples are used to demonstrate that the proposed importance measures can effectively describe the effect of the basic variable on the reliability of the structure system, and the established solution can obtain the two importance measures simultaneously with only a single set of model runs, which allows for a strong reduction of the computational cost.