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The application of reliability sensitivity analysis (RSA) to the high voltage direct current (HVDC) transmission systems is one of the hot topics in the future. A regional RSA method, the contribution to failure probability (CFP) plot, is investigated in this paper. This CFP plot contains both aleatory and epistemic uncertain variables modeled as random variables by probability theory and interval variables by evidence theory, respectively. A surrogate model of second-level limit state function needs to be established for each joint focal element (JFE), which is a time-consuming process. Additionally, an excessive number of Monte Carlo simulations (MCS) and optimizations may exceed the computing power of modern computers. In order to deal with the above problems and further decrease the computational cost, a more effective CFP calculation method under the framework of random-evidence hybrid reliability analysis is proposed. Three important improvements in the proposed method make the calculation of CFP more efficient and easy to implement. Firstly, an active learning kriging (ALK) based on the symbol prediction idea is employed to directly establish a surrogate model rather than a second-level limit state function with fewer function calls, which greatly simplifies construction of the model. Secondly, a random set-based Monte Carlo simulation (RS-MCS) is used to handle the issue of oversized optimization caused by too many JFEs. Thirdly, for further reducing the size of optimizations and improving the efficiency of the CFP calculation, a Karush-Kuhn-Tucker-based optimization (KKTO) method is recommended in the proposed method to solve the extreme value of performance function. A numerical example and an engineering example were studied to verify the accuracy, effectiveness and practicality of the proposed method. It can be seen from the results that regardless of whether it is modeling or computational efficiency, the proposed method is better than the original method. Full article