Statistical two-level model of the production process

Abstract

The mathematical model of economical-manufacturing systems with mass production output was constructed. The state of any production system at any time moment is usually given as a point in two-dimensional phase space. The distribution function for the base product is input, and the equation, being analogous to the kinetic equation in Physics, is put down. Both the engineering-production and the generative functions were determined. The closed system of equations for the distribution function moment was put down in the zero approximation. For the closed system of equations of the manufacturing system’s macroscopic state was obtained. The conditions of manufacturing systems stable operating were written down. The connection between the surplus and the pace of base products motion lengthwise the technological chain was shown. The manufacturing process’ disturbed state system of equations for the particular case of the stability theory (the case of one zero roots of the system’s characteristic equation) was considered.