Wang, Qiang; Zhang, Yufeng; Jin, Ruixing 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 Math. Pract. Theory 37, No. 16, 122-128 (2007). 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 Keywords:stability; reliability; repairable system PDFBibTeX XMLCite \textit{Q. Wang} et al., Math. Pract. Theory 37, No. 16, 122--128 (2007; Zbl 1164.60428)