In industrial system health management, prognostics play a crucial role in ensuring safety and enhancing system availability. While the data-driven approach is the most common for this purpose, they often face challenges due to insufficient training data. This study delves into the prognostic capabilities of four methods under the conditions of limited training datasets. The methods evaluated include two neural network-based approaches, Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM) networks, and two similarity-based methods, Trajectory Similarity-Based Prediction (TSBP) and Data Augmentation Prognostics (DAPROG), with the last being a novel contribution from the authors. The performance of these algorithms is compared using the Commercial Modular Aero-Propulsion System Simulation (CMAPSS) datasets, which are made by simulation of turbofan engine performance degradation. To simulate real-world scenarios of data deficiency, a small fraction of the training datasets from the original dataset is chosen at random for the training, and a comprehensive assessment is conducted for each method in terms of remaining useful life prediction. The results of our study indicate that, while the Convolutional Neural Network (CNN) model generally outperforms others in terms of overall accuracy, Data Augmentation Prognostics (DAPROG) shows comparable performance in the small training dataset, being particularly effective within the range of 10% to 30%. Data Augmentation Prognostics (DAPROG) also exhibits lower variance in its predictions, suggesting a more consistent performance. This is worth highlighting, given the typical challenges associated with artificial neural network methods, such as inherent randomness, non-intuitive decision-making processes, and the complexities involved in developing optimal models.