Accurate remaining useful life (RUL) prediction of critical components plays a vital role in enhancing the reliability, safety, and operational efficiency of industrial systems. However, the lack of fault-related data in real-world production processes, combined with the inherent time-delay and coupling characteristics of the data, poses significant challenges to the accurate RUL prediction of critical components. To address this small-sample limitation, this study proposes a novel hybrid framework that integrates Gaussian noise-based data augmentation (GDA) with an improved Transformer architecture, aiming to enhance model robustness and representation learning. The GDA module generates synthetic failure patterns through controlled noise injection, effectively expanding training datasets. Then the proposed inverted Transformer incorporates temporal attention mechanisms to model long-range dependencies in multivariate time-series degradation signals. Experiments on the PHM2012 dataset demonstrate that this method effectively alleviates the small sample problem and improves the prediction accuracy to 0.9813.