Prognostics and Health Management (PHM) is essential for maintaining optimal performance in industrial environments. Data-driven methods, particularly those leveraging machine learning and deep learning, have demonstrated effectiveness in PHM-related tasks such as anomaly detection, fault diagnosis, and remaining useful life estimation (RUL). However, the scarcity of precise and labeled information often limits their applicability. In this paper, we introduce a novel approach tailored for cases where only monitoring data is available but very few instances are labeled. The proposed method relies on training a generative model in an unsupervised manner to construct a compressor, which is later used to compute a compressor-based distance metric derived from Kolmogorov complexity. When combined with minimal labeled data, the distance metric can be utilized to perform system health estimation. We demonstrate the effectiveness of the approach through two fleet diagnostic problems, where it surpasses the performance of both supervised and semi-supervised methods. Additionally, our method exhibits consistency in handling partial monitoring information, showcasing its robustness in real-world applications.