Duplicated System Reliability Analysis with a Priority Element

Abstract

The increase in the number of system elements and the constant complication of their functions leads to the need to develop appropriate mathematical models of reliability. The failure of a single system element can have serious consequences and lead to the failure of the entire system, so it is important to consider this element as a priority when building mathematical models. The reliability of systems with a priority element should be ensured primarily to maintain the system's functionality and minimize the impact of element failure. In engineering practice, this is achieved by duplicating the priority element, which is used in pumping stations, radio electronics, and the electric power engineering, where the backup element is renewable energy sources, diesel generators, energy storage systems, etc. The article presents a mathematical model of a duplicated system with a priority element. Based on the theory of semi-Markov processes with a phase space of states, the stationary reliability characteristics of the system are determined. A semi-Markov model with a discrete-continuous phase space of states is constructed, which allowed us to obtain results in a more general form. When constructing the model, it was assumed that random variables describing the failure-free operation and restoration times of all elements of the duplicated system have probability distribution functions of a general type. Using the method of successive approximations, the stationary distribution of the embedded Markov chain is found, which is used to determine the system stationary reliability characteristics. An example of using the obtained formulas in engineering calculations is provided

Please cite this article in English as:

Obzherin Yu.E., Sidorov S.M. Duplicated system reliability analysis with a priority element. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2026, no. 2 (155), pp. 58--79 (in Russ.). EDN: CMQZLG

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