An efficient algorithm for computing the signatures of systems with exchangeable components and applications

ABSTRACT

Computing the system signature is an attractive but challenging problem in system reliability. In this article, we propose a novel algorithm to compute the signature of a system with exchangeable components. This new algorithm relies only on the information of minimal cut sets or minimal path sets, which is very intuitive and efficient. The new results in this article are used to address the problem of the aging property of the system signature in the literature. We further discuss the bounds for the system signature when only partial information is available. The application of these new results to cyberattacks is also highlighted.

Keywords:

• System signature
• shock model
• exchangeable lifetimes
• system reliability

Acknowledgements

The authors are very grateful to the Editor and anonymous referees for their insightful and constructive comments that have led to an improved version of this article.

Additional information

Funding

G. Da is supported by the National Nature Science Foundation of China (NSFC 71671177), and P.S. Chan is supported by the Research Grant Council of Hong Kong (GRF 14201015).

Notes on contributors

Gaofeng Da

Gaofeng Da received his Ph.D. degree from Lanzhou University in 2010. He is currently an associate professor in the College of Economics and Management at Nanjing University of Aeronautics and Astronautics, Nanjing, China. His research interests include mathematical reliability and modelling cyber security. He can be reached at [email protected].

Maochao Xu

Maochao Xu is an associate professor of mathematics at Illinois State University. He received his Ph.D. in statistics from Portland State University in 2010. His research interests include statistical modeling, cyber security modeling and risk analysis, and ensuring cyber security. He currently serves as an associate editor for Communications in Statistics. More information about his research can be found at https://sites.google.com/site/maochaoslab/

Ping Shing Chan

Ping Shing Chan received B.Sc., M.Sc., and Ph.D. degrees from McMaster University, Hamilton, ON, Canada, in 1988, 1989, and 1993, respectively. He joined the Chinese University of Hong Kong, Hong Kong, in 1992, where he is currently an associate professor in the Department of Statistics. His research interests include reliability and statistical inference.