The aim of the paper is to improve the quality management system, in the field of the family business succession process management, with the application of TRIZ contradiction modelling. In this work, the authors focus on cognitive activity in contradictions modelling, which is the basis for the first two stages of ARIZ85C, i.e., analysing the problem and analysing the problem model. The application of TRIZ contradiction modelling in the field of quality management is discussed. The selected methods of the acquisition of contradictions are analysed. To identify the contradictions in management systems the method which facilitate the implication of quantitative approach using Grey Incidence Analysis is developed. As a result, the information about the system components and their interactions, functions, contradictions and about the degree of grey incidence between the system components and the system as a whole is obtained. The proposed concept of contradiction modelling is applied and tested in selected family enterprise.