Fundamentals of the statistical theory of the construction of continuum models of production lines
The class of models of production systems with in-line production organization, introduced by the author (2003) and widely used nowadays for constructing effective control systems of production lines is discussed in the paper. Conceptual provisions of the statistical theory of production lines, operating in the transient and steady modes are considered. New types of models that allow to combine the self-consistent object-technology at the micro-level and flow at the macro-level descriptions of the production line are proposed. To build unsteady equations of state of the production line, analytical design methods of technological trajectories of objects of labor are developed. The design methods of technological trajectories are based on the laws of conservation of the number of transferred technology resources on the object of labor at a given space-time structure of the technological process. The developed design methods of technological trajectories were used to construct continuum models of production lines that operate in transient modes. To describe the stochastic process of the transfer of technology resources on the object of labor, the distribution function of objects by states is introduced. A kinetic model of transient processes, the equation of which for the first time contains terms that take into account the normative technological trajectories of objects of labor, and the mechanism of interaction of objects of labor among themselves and the process equipment is constructed. Using the kinetic equation, multi-moment balance equations of the continuum flow model of the production line are written. It is shown that the equations of the model of object-technology description are interrelated and coordinated with the balance equations of continuum flow models through the level of the kinetic description of the production process.