Analysis of QMS development of Russian enterprises shows that efficiency of registered QMS is low enough. The main reasons for ineffective implementation of the QMS are: the formal implementation of QMS, the lack of integration of quality management processes with the overall enterprise management processes, poor understanding of the essence of TQM principles and their non-systemic application. Without underestimating the value of all 8 principles of quality management (according to international standard ISO 9000-2015 there are 7 principles now) which are embodied in the ideology of the ISO standard , the underestimation of the importance of the main leader in the creation and operation of the QMS is a decisive factor in the low-efficiency of many systems. Solving the problem of ensuring and enhancing of management responsibility in accordance with the requirements of international standards ISO 9000 is one of the key issues in the development, implementation and improvement of QMS at Russian enterprises. This article has formed the theory of identification of administrative processes of the enterprise Quality Management System (“Management responsibility” QMS process group) as an object of evaluation and enhancing of the operating effectiveness of the QMS of an industrial enterprise. The author proposes the concept of evaluation and improvement of the operating efficiency of industrial enterprise quality management system. The general result of the study is the solution of scientific problem of theoretical apparatus developing to assess and manage the quality management system operating efficiency as a factor of sustainable development and improvement of Russian enterprises' competitiveness.