Research on prognosis and health management (PHM) technology is actively being conducted. Existing diagnostic technologies focus on qualitative results, i.e., anomaly detection and classification for maintenance. Therefore, quantified diagnostic solutions are required to allow users to take clear actions in advance. In this paper, we propose a diagnostic design solution methodology from a system design perspective, considering the degradation and uncertainty of the system via combined data-driven and model-based approaches using domain adaptation and designable data augmentation. When designing a new target system similar to an existing developed source system, the uncertainty of the diagnostic knowledge of the existing source system is quantified to adapt the domain knowledge to the new target system through Bayesian transfer learning. Additionally, with small amount of target data, a deep-learning-based design algorithm is used to estimate the system design solutions. To validate the proposed method, a case study was conducted using mathematical and Modelica-based physical system models. We verified that the system response obtained from the estimated design solution is more likely to belong to the normal class than to the initial design.