The global sensitivity based on quantile fractile and its solution

In order to investigate the effect of uncertainties of input variables on the quantile fractile the upper limit of the output performance of the products which satisfy a given probabilistic request, a global sensitivity analysis (GSA) index of the input variables based on the quantile fractile was defined. Under a given specific probability value, this sensitivity index can be used to completely assess the average effect of the input variables on the quantile fractile of the output performance when the input variables vary in their distribution ranges. Furthermore, the inherent relationship between the defined index and the existing distribution function (DF) based GSA index and the existing failure probability based GSA index was derived, and a method based on the concept of dimension reduction, a maximum entropy algorithm using fractional moments and the Nataf transformation method were used to efficiently calculate the proposed index. At last, one numerical example and two engineering examples were introduced to show the significant meaning of the proposed GSA index and demonstrate the precision and the efficiency of the proposed computational method simultaneously.