The ordering importance measure of random variable and its estimation

Based on the importance analysis with independent random variables, an ordering importance measure is proposed to evaluate the effects of variables on the uncertainty of output response first, in which not only independent random variables but also correlated ones are included, and it provides a theoretical basis to improve a system or a model. Secondly, the sampling strategy of the conditional probability density function is provided by the Copula transformation, which could solve the vital problem of the importance analysis effectively with correlated random variables. What's more, Due to the low efficiency and tremendous computational cost of the Monte Carlo method, the probability density function evolution method (PDEM) is utilized to solve the ordering importance measure. Finally, some examples in cases of independent random variables and correlated random variables are employed to demonstrate the feasibility and reasonability of the proposed measure, test the precision of the probability density function evolution method, even.