具预警状态的两相同部件并联冗余可修复系统可靠度研究

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周莉,魏连锁,芦雪娟.具预警状态的两相同部件并联冗余可修复系统可靠度研究[J].,2020,60(3):325-330

具预警状态的两相同部件并联冗余可修复系统可靠度研究

Study of reliability of parallel redundant repairable system with two identical components under early warning state

DOI：10.7511/dllgxb202003014

中文关键词:预警状态可修复系统可靠度数值计算

英文关键词:warning state repairable system reliability numerical calculation

基金项目:国家自然科学基金资助项目(1177137461571150)；黑龙江省自然科学基金资助项目(LH2019F037F2017029).

作者	单位
周莉,魏连锁,芦雪娟

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中文摘要:

研究了具有预警状态的两相同部件并联冗余可修复系统的可靠度．可修复系统的可靠度是指系统在规定条件下和时间内完成规定功能的概率．利用泛函分析理论及c0半群理论将原系统的偏微分、积分方程组转化成Banach空间中抽象的Cauchy问题，得到系统的瞬态可靠度和稳态可用度；并证明了该系统具有可靠性和零状态可控性．最后利用Maple软件模拟出系统瞬态可靠度和稳态可用度相应的图形．结果表明：数值模拟和数值计算所得的结论和上述理论证明的结果是一致的，从而可以为两相同部件并联等一类可修复系统的最优控制研究提供参考依据．

英文摘要:

The reliability of parallel redundant repairable system with two identical components under early warning state is studied. The reliability of the repairable system refers to the probability that the system completes the specified function under the specified conditions and time. The functional analysis theory and c0 semi-group theory are used to transform the partial differential and integral equations of the original system into abstract Cauchy problems in Banach space, then the transient reliability and steady-state availability of the system are obtained. And it is proved that the system has reliability and zero state controllability. Finally, the corresponding diagrams of the transient reliability and steady-state availability of the system are simulated by Maple software. The results show that the conclusions obtained by numerical simulation and numerical calculation are consistent with the results proved by the above theory. It can provide reference for the study of the optimal control of a kind of repairable system such as parallel connection of two identical parts.

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具预警状态的两相同部件并联冗余可修复系统可靠度研究

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