Reliability analysis of a repairable duplex system

Abstract

We analyse the survival time of a repairable duplex system characterised by cold standby and by a pre-emptive priority rule. We allow general probability distributions for failure and repair. Moreover, an important realistic feature of the system is the general assumption that the non-priority unit has a memory. This combination of features has not been analysed in the previous literature. Our (new) methodology is based on a concatenation of a Cauchy-type integral representation of the modified Heaviside unit-step function and a two-sided stochastic inequality. Finally, we introduce a security interval related to a security level and a suitable risk-criterion based on the survival function of the system. As a practical application, we analyse some particular cases of the survival function jointly with the security interval corresponding to a security level of 90.

Keywords:

• cold standby
• priority rule
• survival function
• risk-criterion
• security interval
• security level

Acknowledgements

The authors thank the anonymous referees and the Associated Editor of the journal for their valuable suggestions. This research is funded by National Research University Project of Thailand Office of Higher Education Commission and the Center of Biomedical Engineering of Thammasat University.

Additional information

Notes on contributors

E.J. Vanderperre

Edmond J. Vanderperre received his M.Sc. degree (cum laude) in Pure Mathematics from the University of Louvain (1969) and the Dr.Sc. degree (summa cum laude) in Applied Mathematics from the University of Brussels (1981). In 1982, he became a scientific adviser of the Belgian Government for Foreign Affairs (Technical Cooperation). He is currently a visiting professor at the University of South Africa. His present research interest includes the reliability, quality and safety of technical systems.

S.S. Makhanov

Stanislav S. Makhanov received the M.Sc degree in Applied Mathematics from the Moscow State University in 1981 and the Dr.Sc. degree from the Computing Center of the Russian Academy of Science in 1988, where he worked as an Associate Professor until 1993. From 1994 to 1999, he was a Visiting Professor with King Mongkut’s Institute of Technology, Ladkrabang and Associated Faculty with the Asian Institute of Technology of Thailand. He is currently a Full Professor and a Head of a Center of Biomedical Engineering with Sirindhorn International Institute of Technology, Thammasat University of Thailand. He is teaching courses in Applied Mathematics and Computer Science. Dr. Makhanov has published more than 100 research papers and conference proceedings in CAD/CAM, robotics, reliability and medical image processing. He has been a consultant to UN (ESCAP) and other international organisations. Dr. Makhanov’s biography has been published by ‘Who is Who in Asia’, 2007, ‘Who is Who in Science and Engineering’, 2008 and ‘Who is Who in the World’, 2005, 2009, 2012.