Purpose <p>The main purpose of this paper is to propose a reliability assessment method based on the Liu process, addressing multi-dimensional cognitive uncertainty in the bivariate degradation features of hydraulic pumps. This method aims at the problem that hydraulic pumps have multiple degradation features and each feature exhibits multi-dimensional cognitive uncertainty. T</p> Methods <p>First, a bivariate degradation model considering multi-dimensional uncertainty is developed using the Liu process, and the corresponding reliability function is derived. Then, a stepwise parameter estimation method is proposed for the bivariate multi-dimensional degradation model, integrating the α-path, least squares, and maximum likelihood estimation methods. Finally, a denoising method for hydraulic pumps’ vibration signals is introduced, utilizing Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) and Hausdorff distance. Performance degradation indicators are then constructed from these signals using Principal Component Analysis (PCA).</p> Results <p>Degradation tests on hydraulic gear pumps validate the effectiveness and accuracy of the proposed method. The results confirm a nonlinear correlation between the two performance features, effectively modeled by the Frank Copula function. The bivariate model, incorporating multi-dimensional cognitive uncertainty, delivers accurate reliability assessments under small-sample conditions. Compared to single-feature models, it provides more conservative reliability estimates.</p> Conclusion <p>This paper proposes a reliability assessment method for hydraulic pumps, incorporating multi-dimensional cognitive uncertainty in bivariate degradation features. This approach enables accurate reliability assessment under small-sample conditions and offers significant value for engineering applications.</p>