Reliability of a retrial system with mixed standby components and Bernoulli vacation

ABSTRACT

This paper studies a $K-out-of-N$ retrial system with mixed standby components and a single repairman under Bernoulli vacation schedule. Such a model is motivated by some machine repair systems in practice. The repairman may either go for a vacation of random length with probability $p$ or stay idle in system with probability $1-p$ after the completion of a repair. If a component fails, it is repaired at once when the repairman is idle, whereas whether the repairman is busy or vacation, the failed components enter into an orbit. The expressions of steady-state availability, reliability function and the mean time to system first failure are obtained by using vector Markov process and Laplace transform theory. Sensitivity analysis and relative sensitivity analysis are provided. An application example of the intelligent automatic system is demonstrated. Finally, some numerical experiments are conducted to show the impacts of system parameters on reliability indexes. The results presented in the paper may be useful for machine repair system engineers.

KEYWORDS:

• Reliability
• availability
• retrial system
• Bernoulli vacation
• standby

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant [No.72071175] and the Natural Science Foundation of Hebei province [No.A2018203088], People’s Republic of China.

Notes on contributors

Sijia Liu

Sijia Liu received the B.S. degree from Hebei University of Science and Technology, Shijiazhuang, China, in 2017. She is currently pursuing the M.S. degree with the School of Science, Yanshan University. Her interests focus on system reliability analysis and optimization.

Linmin Hu

Linmin Hu received the Ph.D. degree in operations research and management science from the School of Economics and Management, Yanshan University, China, in 2014, where he is currently a professor with the Department of Applied Mathematics. He has published more than 30 papers in journals, including Applied Mathematical Modelling, Journal of Intelligent & Fuzzy Systems, Journal of Systems Science & Complexity and other journals. His research interests include system reliability, operations research and stochastic models.

Zhaocai Liu

Zhaocai Liu is currently pursuing the M.S. degree with the School of Science, Yanshan University. Her interests focus on reliability analysis and application of uncertain systems.

Yuyu Wang

Yuyu Wang received the Ph.D. degree in the pure mathematics from the School of Mathematical Science, Nankai University, China, in 2007. She is currently a professor with the College of Mathematical Science, Tianjin Normal University, China. She has published more than 20 papers in journals, including Science China Mathematics, Mathematica Scandinavica, Topology and its applications, and other journals. Her research interests include stable homotopy, computational topology, digital topology, complex system modeling and reliability theory.