Analysis of the influence of distribution parameters on variance distribution

In order to control output variance, the variance contribution of inputs, determined by their distribution parameters, needs to be analyzed, thus the influence of input distribution parameters on variance should be investigated further. Focusing on the classical quadratic polynomial without cross-terms, correlated inputs are transformed into independent ones using the independent-orthogonalisation transformation, then the sensitivity of each input's variance contribution and of the total variance contribution are derived analytically with respect to each distribution parameter. From the analytical solutions, the basic laws of how distribution parameters affect the variance contribution are developed and some explanations are given. At last, numerical and engineering examples are employed to demonstrate the accuracy and rationality of the analytical solutions.