Revised regional importance measures in the presence of epistemic and aleatory uncertainties

Two revised regional importance measures (RIMs), that is, revised contribution to variance of sample mean (RCVSM) and revised contribution to variance of sample variance (RCVSV), are defined herein by using the revised means of sample mean and sample variance, which vary with the reduced range of the epistemic parameter. The RCVSM and RCVSV can be computed by the same set of samples, thus no extra computational cost is introduced with respect to the computations of CVSM and CVSV. From the plots of RCVSM and RCVSV, accurate quantitative information on variance reductions of sample mean and sample variance can be read because of reduced upper bound of the range of the epistemic parameter. For general form of quadratic polynomial output, the analytical solutions of the original and the revised RIMs are given. Numerical example is employed and results demonstrate that the analytical results are consistent and accurate. An engineering example is applied to testify the validity and rationality of the revised RIMs, which can give instructions to the engineers about how to reduce variance of sample mean and sample variance by reducing the range of epistemic parameters.