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

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.