A new kind of regional importance measure of the input variable and its state dependent parameter solution

• Two new regional importance measures (RIMs) of the input variable are proposed.
• The properties of the two proposed RIMs are analyzed and proved.
• The relationships of two proposed RIMs with the existing RIMs are derived.
• The highly-efficient SDP solutions for two proposed RIMs are established.

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.