The work is devoted to the study of the possibilities of ensuring the unconditional achievement of the goals of industrial enterprises with a combination of modal management and linear regulation with cost optimization in the operational and tactical management of quality management systems. The commonality of dependencies in modal control and linear regulation is shown. An approach to the combination of modal control and linear regulation is proposed, including the determination of the possibilities for changing the elements of the system matrix, as well as the search for optimal or rational solutions based on cost accounting. The application of this approach is considered on the example of the activity of an industrial enterprise. It is established that modal control has no advantages over linear control, since it is used to increase the stability of systems. The performance of quality management systems can be ensured when it is transferred to an unstable mode of operation, however, the use of this mode cannot exceed two to three years.

Keywords: quality management system, modal management, linear regulation, optimization, enterprise potential, personnel resistance

Using finite differences, a transition is made from a second-order differential equation to a difference equation to describe the dynamics of the integral indicator of product quality. Relationships between the coefficients of the difference equation of quality dynamics and the second-order autoregression equation for the integral quality indicator are determined. On the basis of experimental data on the dynamics of the integral quality indicator, the adequacy of its description by a second-order linear differential equation, as well as the related linear difference equation and the autoregression equation, is substantiated. The analysis of the results of the activities of three Russian enterprises to ensure the quality of the trolleybuses they produce using a generalized analogue of the sensitivity coefficient, the ratio of the average value of the control action to its range and the pulsation coefficient. The relationship between the results of the activities of these enterprises and their further life cycle is considered.

Keywords: quality dynamics, finite difference method, autoregression, integral quality indicator

For the three main processes of the enterprise, identified in the decomposition of its activities, a mathematical model in the space of conditions is developed, taking into account their relationship and interaction in the quality management system. For the obtained system of differential equations, the structural composition of the operators included in it is disclosed. An example of the application of the created mathematical model in the study of the functioning of the quality management system using linear and non-linear operators and the action of random external disturbances is considered. A discussion of the simulation results at various parameter values from the point of view of the functioning of the selected processes is presented.

Keywords: differential equation, space of conditions, process, quality management system