Studying the Reliability of a Set of Production Elements and Subsystems

The article addresses the task of ensuring the reliability of a set of elements, components, and product kits supplied by vendors for final assembly, as well as the control and monitoring of the condition of elements and subsystems within technological and production systems across the entire supply chain. A study of complex system structures is presented. The system structure is understood as a schematic or mathematical representation of the main system elements, necessary and sufficient to achieve the research objective; a system element is defined as a conditionally indivisible part of the system, with its distinguishing characteristic determined by the research goal; a system connection is understood as a condition defining one of the interactions between system elements. The results of a study of a system with an exponential reliability function and constant recovery time, availability, and its variance for a given number of cycles, a finite time interval, and a steady state are presented. System calculation criteria based on its cost model and including the availability function are defined. Methods for studying the sensitivity of the optimal values of the system’s mean time to failure and mean time to recovery across the entire system are described. It is substantiated that the steady-state availability does not depend on the distributions of system time to failure and recovery time and, over a finite time interval, is determined by the mathematical expectation of the failure-free operation time fraction. Approximations for the distribution of the steady-state equipment availability are obtained, which, together with economic factors, can be used to decide whether to launch the system during the first cycle or in the initial period. The results of a study on the problem of optimal system design considering economic factors and the steady-state availability function are presented. It is concluded that the research results can be practically implemented using modern digitalization tools to systematize quality control information for complex production structures, machine complexes, and other complex technical and technological systems.