Robotic assembly systems traditionally require substantial manual engineering effort to integrate new tasks, adapt to new environments, and improve performance over time. This paper presents a framework for autonomous integration and continuous improvement of robotic assembly systems based on Skill Graph representations. A Skill Graph organizes robot capabilities as verb-based skills, explicitly linking semantic descriptions (verbs and nouns) with executable policies, pre-conditions, post-conditions, and evaluators. We show how Skill Graphs enable rapid system integration by supporting semantic-level planning over skills, while simultaneously grounding execution through well-defined interfaces to robot controllers and perception modules. After initial deployment, the same Skill Graph structure supports systematic data collection and closed-loop performance improvement, enabling iterative refinement of skills and their composition. We demonstrate how this approach unifies system configuration, execution, evaluation, and learning within a single representation, providing a scalable pathway toward adaptive and reusable robotic assembly systems. The code is at https://github.com/intelligent-control-lab/AIDF.