The Spectrum of A Parallel Repairable System with Warm Standby
نویسندگان
چکیده
Abstract: In this paper, the spectrum of a parallel repairable system with warm standby is investigated. Firstly, we formulate the problem into a suitable Banach space. Then we carry out a detailed spectral analysis of the system operator. Based on the spectral analysis and C0 semigroup theory, we prove the existence of positive solution and finite expansion of the solution corresponding to its eigenvector. As a consequence we get that its dynamic solutions converges exponentially to the stead-state solution. Finally, we obtain the finite expansion of solution and derive some reliability indices of the system.
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