The evaluation and accreditation of competencies is one of the challenges that higher education must address in the 21st century. GRAF is a system of evaluation and accreditation of curricular competencies based on the integration of pedagogical engineering methodologies with data architecture design and technological applications, especially tailored to online higher education. From the teaching point of view, it provides a model, a methodology, and a tool for designing competency-based programmes and assessing the evidence of competency learning generated by the students in the teaching and learning process throughout the semester. From the student's perspective, it enhances conventional evaluation by accompanying marks with educational feedback on the level of competency achieved, and provides a graphic representation of progress. Specific tools and applications have been developed for each phase of work: for the design stage, the Competency Design Tool; for the evaluation and monitoring stage, the Competency Assessment Tool; and for the graphic representation stage, the Competency Graph Report. The Universitat Oberta de Catalunya (UOC) has spent two years developing GRAF. It has been applied to five programmes in different areas: an MBA, two master's degrees, a postgraduate course, and a university extension course. A total of 56 compulsory subjects and 293 students have been involved in these programmes. Due to the success of the initiative, the UOC has decided on a widespread application of GRAF to other programmes. We are interested in sharing the experience and lessons learned in order to improve GRAF.