Spectral analysis of a two unit deteriorating standby system with repair
Spectral analysis of a two unit deteriorating standby system with repair
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发表时间：
2011-04
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通讯作者：
Wenzhi Yuan;Genqi Wu
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作者：
Wenzhi Yuan;Genqi Wu
在本文中，我们分析了由工作单元和修复单元组成的系统的频谱和稳定性，其中工作单元由一个主单元和一个备用单元组成，而备用单元在备用模式下可能会恶化。首先，我们将问题表述为合适的 Banach 空间。然后我们对系统算子进行详细的谱分析。基于谱分析和C0半群理论，根据其特征向量证明了正解的存在性和解的有限展开式。因此，我们得到它的动态解以指数方式收敛到稳态解。最后，我们得出了系统的一些可靠性指标。
In this paper, we analyze the spectra and stability of a system consisting of a working unit and repair unit, in which the working unit consists of one main unit and one standby unit, while the standby unit may deteriorate in its standby mode. Firstly, we formulate the problem into a suitable Banach space. And 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 according to its eigenvectors. As a consequence we get that its dynamic solutions converges exponentially to the steady-state solution. Finally, we derive some reliability indices of the system.