Dynamic analysis of a deteriorating system with single vacation of a repairman
Dynamic analysis of a deteriorating system with single vacation of a repairman
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修理工单次休假情况下恶化系统的动态分析
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通讯作者：
Muhtabar Muhtar
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作者：
Qi Xueping;Abdukerim Haji;Muhtabar Muhtar
研究了一类修理工单重休假的退化系统。该系统由带边界条件的无穷微分-积分方程描述。首先，利用泛函分析的方法，特别是线性算子的C 0 -半群理论，证明了系统的适定性和存在唯一的满足概率条件的正动力学解。其次，通过分析系统算子的谱性质，证明了虚轴上除零点外的所有点都属于系统算子的预解集。最后，我们证明了零不是系统算子的本征值，这意味着系统的稳态解不存在。
In this paper, we investigate a deteriorating system with single vacation of a repairman. The system is described by infinite differential-integral equations with boundary conditions. Firstly, by using functional analysis methods, especially linear operator’s C 0 -semigroup theory, we prove the well-posedness of the system and the existence of a unique positive dynamic solution that satisfies probability condition. Next, by analyzing the spectral properties of the system operator, we prove that all points on the imaginary axis except zero belong to the resolvent set of the system operator. Lastly, we prove that zero is not an eigenvalue of the system operator, which implies that the steady-state solution of the system does not exist.