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Asymptotic stability and reliability analysis of a repairable system with a deteriorating standby unit under common-cause failure and critical human error. (Chinese. English summary) Zbl 1164.60428

Summary: This paper presents the model of a repairable system with a deteriorating standby unit under common-cause failure and critical human error. First, we discuss and prove the asymptotic stability of the solution of the system, that is, \(\lim\limits_{t\to\infty}\vec P (\cdot, t)=\vec P\). Then, we finish the proof of reliability of the system.

MSC:

60K10 Applications of renewal theory (reliability, demand theory, etc.)
90B25 Reliability, availability, maintenance, inspection in operations research
62N05 Reliability and life testing
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