Uncertainty reduction is vital for improving system reliability and reducing risks. To identify the best target for uncertainty reduction, uncertainty importance measure is commonly used to prioritize the significance of input variable uncertainties. Then, designers will 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 should also be considered in developing uncertainty reduction strategies. Although variance-based methods have been developed for this purpose, they are dependent on statistical moments and have limitations when dealing with highly-skewed distributions that are commonly encountered in practical applications. Motivated by this problem, we propose a new uncertainty importance measure based on cumulative residual entropy. The proposed measure is moment-independent based on the cumulative distribution function, which can handle the highly-skewed distributions properly. Numerical implementations for estimating the proposed measure are devised and verified. A real-world engineering case considering highly-skewed distributions is introduced to show the procedure of developing uncertainty reduction strategies considering uncertainty magnitude and corresponding cost. The results demonstrate that the proposed measure can present a different uncertainty reduction recommendation compared to the variance-based approach because of its moment-independent characteristic.

翻译：不确定性削减对于提升系统可靠性和降低风险至关重要。为确定不确定性削减的最佳目标，通常采用不确定性重要度测度来评估输入变量不确定性的相对重要性。随后，设计人员将采取措施降低高重要性变量的不确定性。然而，对于不确定性极小的变量，控制其不确定性的成本可能难以接受。因此，在制定不确定性削减策略时亦需考虑不确定性的量级。尽管已有基于方差的方法用于此目的，但这些方法依赖于统计矩，且在处理实际应用中常见的高度偏态分布时存在局限。受此问题启发，我们提出一种基于累积剩余熵的新不确定性重要度测度。该测度基于累积分布函数构建，具有矩独立性，能够妥善处理高度偏态分布。本文设计并验证了估计该测度的数值实现方法。通过引入考虑高度偏态分布的实际工程案例，展示了兼顾不确定性量级与相应成本的削减策略制定流程。结果表明，由于所提测度的矩独立特性，其给出的不确定性削减建议与基于方差的方法存在显著差异。