Analysis of a multi-component system with double threshold control policy

Abstract

This paper investigates a multi-component repairable system with double threshold control policy. The system is composed of n identical and independent components which operate simultaneously at the beginning, and it is down when the number of operating components decreases to $k-1(k⩽n)$. When the number of failed components is less than the value L, the repairman repairs them with a low repair rate. The high repair rate is activated as soon as L failed components present, and continues until the number of failed components drops to the value N−1. Applying the matrix analytical method, the Laplace transform technique and the properties of the phase type distribution, various performance measures including the availability, the rate of occurrence of failures, and the reliability are derived in transient and stationary regimes. Further, numerical examples are reported to show the behaviour of the system.

Keywords:

• Multi-component system
• double threshold control policy
• matrix analytical method
• reliability measures

Acknowledgments

The authors acknowledge anonymous reviewers for their constructive comments which are very helpful in improving the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the National Natural Science Foundation of China (No. 71571127), the funding of V.C. & V.R. Key Lab of Sichuan Province (SCVCVR2019.05VS), and the Sichuan Science and Technology Program (Nos. 2020YFS0318, 2019YFS0155, 2019YFS0146, 2020YFG0430, 2020YFS0307).

Notes on contributors

Wenqing Wu

Wenqing Wu was born in 1986. He obtained both M.S. and D.Sc degree in Applied Mathematics from Sichuan Normal University, Chengdu, China, in 2012 and 2015, respectively. His current research interests include reliability analysis and grey forecasting model. Email: [email protected].

Gang He

Gang He received the B.S. degree in Engineering Mechanics from Sichuan University, Chengdu, China, in 2006. He worked as Post doctorate at Sichuan University in the field of First principle calculations on Titanium materials. He worked as a lecturer at Southwest University of Science and Technology since 2015. Email: [email protected].

Wenxin Yu

Wenxin Yu received the B.S. degree in Shanghai Jiaotong University in 2006, and the M.S. and Ph.D. degree in System LSI from Waseda University, Kitakyushu, Japan, in 2010 and 2014. He has authored or co-authored over 40 papers in international journals and conferences. His current research interests include 3D multi-view synthesis, neural network, reliability, video decoding algorithm. Email: [email protected].

Mengxin Wang

Mengxin Wang is a graduate student in the Zhongtai Securities Institute of Financial Studies, Shandong University. Her research interests are focussed on financial mathematics and deep learning. Email: [email protected]; [email protected].

Kang Xu

Kang Xu was graduated in Computer Science from University of Science and Technology of China. He is working in the computer college of Southwest University of Science and Technology now. His research interests are focussed on Computer Control and Pattern Recognition. Email: [email protected].