Contents I. Introduction
Nowadays mathematical models are widely used for simulation in many fields, such as structural reliability, performance evaluation of mechanics, or nuclear safety, behavior of power grid, as practical experiments are often expensive or even impracticable. As the complexity of these models keeps increasing, it becomes more often than ever before when engineers have to take all the inputs into consideration thoroughly and find which of them are more important to the model. SA(sensitivity analysis)[1], is exactly proposed to quantify the relative importance of each input variable in determining the value of an assigned output. The family of importance measure generally include nonparametric techniques suggested by Saltelli, Marivoet and Iman et al. variance-based methods, which suggested by Sobol and further developed by Rabitz and Alis, are based on the HMDR[3] [4] for a simple reason that high order correlated effects of the inputs are expected to have negligible effect on the output (i.e., a multivariate function representing a multidimensional physical output can often be approximated to good accuracy by a sum of functions with each function having fewer variables)[2]. In a addition, the researchers proposed a series of methods to obtain the variance based importance measures more efficiently, such as single-loop MCS (Monte Carlo simulation), quasi- MCS et al[5]–[7]. However, the drawback, to decompose the variance contribution by the input to the model output based on HMDR, is that contribution of the individual input itself may include others' contribution. (ie: a unclear decomposition for the variability contribution of to model output.)
