Mathematical Models of the Processes of Operation, Renewal and Degradation of a Fleet of Complex Technical Systems with Metrological Support.

(1) Background: The aim of the study is to develop a set of models for managing a fleet of complex technical systems with metrological support, allowing the simulation and management at all the stages of the life cycle of the complex technical systems, as well as to simulate the functioning of large fleets of complex technical systems, including up to several hundred thousand samples; (2) Methods: The authors use methods of mathematical modeling, methods of the theory of Markov and semi-Markov processes, methods of optimization, methods of reliability theory, and methods of probability theory and mathematical statistics; (3) Results: an interconnected set of mathematical models for managing a fleet of complex technical systems with metrological support was developed and the applied software was developed; (4) Conclusions: The set of models presented in the article allows for the adequate simulation of all the stages of the life cycle of large complex technical systems fleets, including up to several hundreds of thousands of samples, to optimize the functioning processes of a fleet of complex technical systems, to form strategies for fleet development, and to assess the risks associated with false and undetected failures, as well as the risks associated with the degradation of complex technical systems. [ABSTRACT FROM AUTHOR]