<p>Bearings are widely used components in rotating systems across various industries, making their health monitoring critical. Over the past decade, extensive research has been conducted in this field. However, most signal processing approaches for bearing fault detection have been developed under the assumption of Gaussian noise, which is not ideal for machines operating in harsh environments such as mining or aviation. These machines are often exposed to heavy-tailed noise, which poses challenges for traditional signal-processing techniques based on Gaussian-noise assumptions. In this study, we propose a robust ensemble empirical mode decomposition (REEMD) technique to handle heavy-tailed noise. The proposed approach utilizes a moving median-based sifting process with adaptive window sizes to calculate the upper and lower envelopes, thereby providing enhanced robustness against heavy-tailed noise. The performance of the proposed method was evaluated through simulations with varying levels of heavy-tailed noise and compared with established decomposition methods. Additionally, two real-world data sets are used to demonstrate the effectiveness of the proposed approach in practical scenarios.</p>