可修复系统解的渐近稳定性及最优检测时间

徐厚宝;柳合龙;朱广田

系统科学与数学 ›› 2008, Vol. 28 ›› Issue (3) : 265-274.

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PDF(373 KB)
系统科学与数学 ›› 2008, Vol. 28 ›› Issue (3) : 265-274. DOI: 10.12341/jssms10066
论文

可修复系统解的渐近稳定性及最优检测时间

    徐厚宝(1),柳合龙(2), 朱广田(3)
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Well Posedness and Optimal Check Time of a Repairable System

    XU Houbao(1),LIU Helong(2), ZHU Guangtian(3)
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摘要

应用C0半群理论,证明了服从一般分布的可修复系统的唯一非负时间依赖解的存在性,并指出该解恰是系统算子的0本征值对应的规范化后的本征向量.然后基于系统静态可用度,给出了系统检测时间和系统静态可用度之间的关系表达式,并分析了系统最优检测时间的存在性.

Abstract

The existence of optimal check time of a repairable system with repair time following general distribution is studied. First, the unique existence of the solution of such system is proved. Then, by the positive C0-semigroup generated
by system operator, it is shown that there exists a steady nonnegative solution of the system which is just the normalized eigenvector corresponding to
eigenvalue 0 of system operator. At last, based on steady availability of the system, the existence of optimal check time is given.

关键词

C0半群 / 适定性 / 最优检测时间.

Key words

C0-semigroup / well posedness / optimal check time.

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徐厚宝 , 柳合龙 , 朱广田. 可修复系统解的渐近稳定性及最优检测时间. 系统科学与数学, 2008, 28(3): 265-274. https://doi.org/10.12341/jssms10066
XU Houbao , LIU Helong , ZHU Guangtian. Well Posedness and Optimal Check Time of a Repairable System. Journal of Systems Science and Mathematical Sciences, 2008, 28(3): 265-274 https://doi.org/10.12341/jssms10066
中图分类号: 93D25    34D35   
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