RECURSIVE APPROACHES TO RELIABILITY ASSESSMENT OF RING STRUCTURES

The problem of assessing the reliability of ring structures is highly relevant for many engineering systems, such as water supply, gas, telecommunication, and energy networks. This article is devoted to the analysis of the topological characteristics of ring networks, their impact on failure resilience, and the development of mathematical models for reliability assessment. Particular attention is paid to single-ring structures, considering both uniform and varying reliability of elements. Based on graph theory and spanning trees, formulas are proposed that take into account all possible combinations of element functionality and the contribution of redundant paths. Special focus is given to the development of recursive models, which significantly simplify numerical calculations and enable the modeling of large systems with numerous elements. The tabular representation of network states demonstrates all possible functionality configurations, facilitating accurate prediction of network behavior under partial failures. The practical significance of this study lies in the creation of universal tools for engineering network design, cost optimization, risk reduction, and enhanced system resilience. The proposed models can be applied to local networks, systems with redundant lines, and telecommunication structures. An important direction for future research is the development of dynamic models that consider changes in reliability parameters over time. The results presented lay the foundation for improving the operational efficiency of real-world systems in various industrial sectors.