Economic and political changes in contemporary society lead to reforms of many social spheres. The system of education in general and higher professional education in particular is no exception. The issue of ensuring the quality of education has recently attracted great attention in all countries of the world. The key problem of reforming education is raising its quality. In this paper, the object of research was the quality of education provided by higher education institutions. The authors have conducted the analysis of models for raising the quality of education and qualimetry of the laboratory work quality based on a survey of teachers and students. The QFD method was described by the example of its application in five universities of the Russian Federation. It has been proved that this method can provide the university with a planning tool with which higher education institutions can provide services that fully meet the requirements of customers (students, parents, employers, the state and society as a whole), thereby ensuring the suitability of the system to meet external requirements -- the Fitness-for-Purpose approach (building goals based on the external environment). In addition, it has also been substantiated that the application of this method in the system of higher professional education will ensure the suitability of the system to achieve its own goals -- the Fitness-for-Purpose approach (development, improvement, effective management). Thus, the QFD method will make it possible to support of all types of coordinated activities for the leadership and management of higher education institutions in relation to quality, as well as a set of developed regulatory and methodological documents that determine the content, technologies, methods and means of work of all officials, teachers and students to further improve the quality of educational process, thereby ensuring the competitiveness of higher education institutions and effective development on the global market of educational services.