#### Ehmet Kasim, The exponential stability of a two-unit system with non-preemptive priority, Vol. 2022 (2022), Article ID 28, pp. 1-24

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DOI: 10.23952/jnfa.2022.28

Received February 14, 2022; Accepted June 7, 2022; Published July 20, 2022

Abstract This study analyzes a repairable system with two dissimilar units, one of which has non-preemptive priority. We transform the model to an abstract Cauchy problem and study the well-posedness via the $C_0-$ semigroup theory of linear operators. By using spectral properties of the corresponding operators, we derive the exponential convergence of the time-dependent solution to its steady-state solution. We also present the asymptotic behavior of several time-dependent reliability indices and numerical examples.