Importance measures of basic random variable and their probability density evolution solutions

To improve the current analysis of basic variable importance, a new moment independent importance measure system, including total importance measure, mean total importance measure, main importance measure and mean main importance measure, is established based on the present single moment independent importance measure. Those indices are used to evaluate the effects of basic random variable on the whole uncertainty of the output of system or model under different requirements. After definitions of those importance measures are given, their engineering significations and applications are illustrated in detail. The solution of the proposed measures is provided based on the probability density evolution method due to its merits. Two examples are used to demonstrate that the proposed importance measure system is more reasonable than the existing systems, and the proposed solution can improve computational efficiency substantially with acceptable precision.