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However, complex working conditions and high-cost data collection inherent in real-world scenarios pose small-data challenges for the application of these methods. Given the urgent need for data-efficient PHM techniques in academia and industry, this paper aims to explore the fundamental concepts, ongoing research, and future trajectories of small data challenges in the PHM domain. This survey first elucidates the definition, causes, and impacts of small data on PHM tasks, and then analyzes the current mainstream approaches to solving small data problems, including data augmentation, transfer learning, and few-shot learning techniques, each of which has its advantages and disadvantages. In addition, this survey summarizes benchmark datasets and experimental paradigms to facilitate fair evaluations of diverse methodologies under small data conditions. 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