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Abstract: To further analyze the effect of different regions within input variable on the variance and mean of the model output, two new regional importance measures (RIMs) are proposed, which are the “contribution to variance of conditional mean (CVCM)” and the “contribution to mean of conditional mean (CMCM)”. The properties of the two RIMs are analyzed and their relationships with the existing contribution to sample variance (CSV) and contribution to sample mean (CSM) are derived. Based on their characteristics, the highly efficient state dependent parameter (SDP) method is introduced to estimate them. By virtue of the advantages of the SDP-based method, the same set of sample points utilized for solving CSM and CSV is enough to estimate CVCM and CMCM. Several examples demonstrate that CVCM can provide further information on the existing CSV, which can effectively instruct the engineer on how to achieve a targeted reduction of the main effect of each input variable. CMCM can act as effectively as the CSM, but the convergence and stability for estimating CMCM by numerical simulation is better than those for estimating CSM. Besides, the efficiency and accuracy of the SDP-based method are also testified by the examples. [Copyright &y& Elsevier]

Abstract: Variance based sensitivity indices represent how the input uncertainty influences the output uncertainty. In order to identify how the distribution parameters of inputs influence the variance contributions, this work proposes the sensitivity of the variance contributions, which is defined by the partial derivative of the first-order variance contribution with respect to the distribution parameter. The proposed sensitivity can reflect how small variation of the distribution parameter influences the first-order variance contribution. By simplifying the partial derivative of the first-order variance contribution into the form of expectation via the kernel function, the proposed sensitivity can be seen as a by-product of the variance based sensitivity analysis without any additional output evaluations. For the classical quadratic responses, the proposed sensitivity can be derived analytically based on the integral form, while for the complex responses, the state dependent parameter (SDP) based method, which has been applied in the variance sensitivity analysis, can be employed to compute the proposed sensitivity. Several examples are used to demonstrate the correctness of the analytical solutions and the efficiency of the SDP based method. [Copyright &y& Elsevier]