Trapeznikov’s statistical control paradigm and its application to modeling the functioning of a chaotic industrial system

120th anniversary of the famous domestic Academician V.A. Trapeznikov actualizes the features of his scientific search with commitment to statistical teaching in the study of economic systems’ behavior, which became a prologue to his entropy-informational paradigm of analyzing the effect of their functioning. The entrenched determinism in economics, which dominated the formalization of its classical problems, gave a way to a probabilistic interpretation of the dependence of this effect on the factors it is influencing. It makes possible to identify and interpret the inherent patterns of behavior and dynamics of uncertainty indicators, organization, and effect of industrial systems in the symbiosis of natural sciences and economics. The aim of the present study is to increase knowledge about the statistical nature of the functioning of the industrial system; it is displayed by its entropy, information, and economic processes. According to V.A. Trapeznikov’s statistical control paradigm, the article presents its applications in the analysis of Verhulst and Redenur’s logistic models, the construction of a logarithmic model incorporating indicators of information control, disorder, and a given level of system control perfection (according to V.A. Trapeznikov). The obtained condition for the stability of this level in relation to the industrial system with the interpretation of the exponential growth of the input control information is discussed. The level of knowledge of the economic system according to V.A. Trapeznikov, its definition and calculation based on the material of industrial enterprise is characterized. Within the framework of the statistical control paradigm, the article introduces an assessment of the level of control system imperfection of an industrial system, provides a description and interpretation of the developed models of its relationship with disorder and the amount of control information, and with the entropy measure of the system’s functioning in its initial and current states. The areas of ongoing convergent studies on the entropy-informational nature of economic processes are noted.