Reliability characteristics numerical study of a duplicated system with priority

Mathematical modeling of duplicated systems with a priority, consisting of non-homogeneous elements, allows for the derivation of analytical expressions for their reliability analysis. However, in practice, these expressions prove suitable for engineering calculations only in particular cases or for simplified models. The relevance of this research is determined by the aim to obtain such approximate expressions for a semi-Markov model with a state space in a general form. This article is devoted to the reliability characteristics numerical study of a duplicated system with a priority element. The principal research method involves applying the asymptotic phase merging algorithm and the assumption of "fast" restoration of the priority element to a semi-Markov model with a state space in a general form. This approach, in turn, allows for obtaining more general results under general form distributions of element uptimes and restoration times. The article presents formulas that enable the approximate calculation of reliability characteristics for a duplicated system with a priority. The error of the obtained approximate formulas is estimated by comparing them with exact and known results for various distributions of element uptimes and restoration times. The materials presented in the article are of practical value for engineers and researchers involved in the reliability analysis of duplicated technical systems at the stages of their design and operation.

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