Topical Methodologies for Managing Quality and Reliability of Technological Systems, Including Those Containing a Continuous Environment: Review and Critical Analysis

Modern requirements for technical systems and management processes necessitate the use of comprehensive methodological approaches that ensure high standards of quality, reliability, and innovation. In the context of rapid technological progress and the complexity of systems, effective evaluation and decision-making methods based on multiple criteria have become increasingly important. The presented work provides a comprehensive analysis of modern methodologies for managing the quality, reliability, and risks of technological systems, including processes based on the motion of a continuous medium (hydrodynamic, gasdynamic, thermomechanical, and deformation phenomena). The study of universal processes of continuous medium movement in the context of multi-storey infrastructure of enterprises allows for the development of unifi ed approaches to ensuring the quality of products in various industries. The research is based on the principles of system analysis, including a comparative assessment of the effectiveness of methodologies and the identifi cation of synergistic effects when they are integrated. Special attention is given to digital technologies as a catalyst for the evolution of traditional approaches. The results are systematized in the form of classifi cation matrices that refl ect the scope, advantages, and limitations of each methodology. The practical signifi cance of the research is confi rmed by successful implementation cases in key industries, such as aircraft engineering (optimization of the MS-21 design), energy (increasing the reliability of nuclear power plants), the oil and gas sector (predictive maintenance of infrastructure), and the military-industrial complex (calculations for advanced equipment).