Anomaly detection is an essential task for quality management in smart manufacturing. An accurate data-driven detection method usually needs enough data and labels. However, in practice, there commonly exist newly set-up processes in manufacturing, and they only have quite limited data available for analysis. Borrowing the name from the recommender system, we call this process a cold-start process. The sparsity of anomaly, the deviation of the profile, and noise aggravate the detection difficulty. Transfer learning could help to detect anomalies for cold-start processes by transferring the knowledge from more experienced processes to the new processes. However, the existing transfer learning and multi-task learning frameworks are established on task- or domain-level relatedness. We observe instead, within a domain, some components (background and anomaly) share more commonality, others (profile deviation and noise) not. To this end, we propose a more delicate component-level transfer learning scheme, i.e., decomposition-based hybrid transfer learning (DHTL): It first decomposes a domain (e.g., a data source containing profiles) into different components (smooth background, profile deviation, anomaly, and noise); then, each component’s transferability is analyzed by expert knowledge; Lastly, different transfer learning techniques could be tailored accordingly. We adopted the Bayesian probabilistic hierarchical model to formulate parameter transfer for the background, and “L2,1+L1”-norm to formulate low dimension feature-representation transfer for the anomaly. An efficient algorithm based on Block Coordinate Descend is proposed to learn the parameters. A case study based on glass coating pressure profiles demonstrates the improved accuracy and completeness of detected anomaly, and a simulation demonstrates the fidelity of the decomposition results.