Modeling Quality Management Systems by Integrating Diacoptics, Graph Theory and Fractal Analysis

The article describes a new approach to modeling the state of management systems, particularly Quality Management Systems, through the integration of diakoptics, fractal analysis, and graph theory. This relevance of the study lies in integrating three independent methods for analyzing complex mechanical systems. These systems can be described by both continuous linear and discrete-nonlinear or linearized differential equations. The systems can be integrated into single, integral connections, which allow for investigating structures, dynamics and analyzing risks of both individual components and general or entire elements included in the quality management systems. The purpose of the study is to justify the integration of these three mathematical directions in modeling or analyzing the state of complex systems, structures, and technological equipment included in both management systems in general and in quality management systems in particular. The fi ndings of the article are based on theoretical research and validated by the practical application of a risk-based approach to implementing and maintaining any standard from the ISO 9000:2015 family, primarily as required by the foundational ISO 9001:2015 standard. Results. The study established the core goals and objectives of the proposed methodology integrating three methods. The graph theory studies the relationships between objects represented as vertices and edges; the fractal methods describe structures that are self-similar at different scales; and the diacoptics methods are used in analyzing the physical and mechanical properties of technological equipment, which defi nes the quality management systems of high-tech industries based on its components’ characteristics.