A new moment-independent uncertainty importance measure based on cumulative residual entropy for developing uncertainty reduction strategies

Uncertainty reduction is crucial for enhancing system reliability and mitigating risks. To identify the most effective target for uncertainty reduction, uncertainty importance measures are commonly used in global sensitivity analysis to prioritize input variable uncertainties. Designers then take steps to reduce the uncertainties of variables with high importance. However, for variables with minimal uncertainty, the cost of controlling their uncertainties can be unacceptable. Therefore, uncertainty magnitude and the corresponding cost for uncertainty reduction should also be considered when developing uncertainty reduction strategies. Although variance-based methods have been developed for this purpose, they rely on statistical moments and face limitations when handling highly-skewed distributions. Additionally, existing moment-independent methods fail to effectively quantify the uncertainty magnitude and cannot fully support the formulation of uncertainty reduction strategies. Motivated by this issue, we propose a new uncertainty importance measure based on cumulative residual entropy. The proposed measure is moment-independent based on cumulative distribution function, enabling it to handle highly-skewed distributions and quantify uncertainty magnitude effectively. Numerical implementations for estimating the proposed measure are devised and validated. The effectiveness of the proposed measure in importance ranking is verified through two numerical examples, comparing it with the Sobol index, delta index, Gaussian kernel-based index and mutual information. Then, a real-world engineering case involving highly-skewed distributions is presented to illustrate the development of uncertainty reduction strategies considering uncertainty importance and magnitude. The results demonstrate that the proposed measure presents a different uncertainty reduction recommendation compared to the variance-based approach due to its moment-independent characteristic. Our code is publicly available at GitHub: https://github.com/dirge1/GSA_CRE.