This paper shows to what extent data used in design optimization process and TRIZ based models of contradictions can benefit from each other. New design often starts by optimizing existing systems by experimental and numerical means. This approach requires building a model linking on the one hand, a set of Action Parameters; and on the other hand, Evaluation Parameters measuring the quality of a solution. When none of the solutions satisfy the objectives, a redesign of the system is required. Our hypothesis in this paper is that the analysis of experimental or simulation data, can be used as input to automatically extract systems of contradictions, and moreover that it can help to make a ranking of these systems of contradictions.In the article 3 ways to extract, out of Design of Experiments, and to prioritize Generalized Systems of Contradictions will be presented. These methods will be illustrated throughout a case study related to a cutting process.