Graduation formula: a new method to construct belief reliability distribution under epistemic uncertainty

doi:10.23919/JSEE.2020.000038

Journal of Systems Engineering and Electronics ›› 2020, Vol. 31 ›› Issue (3): 626-633.doi: 10.23919/JSEE.2020.000038

• Reliability • Previous Articles Next Articles

Graduation formula: a new method to construct belief reliability distribution under epistemic uncertainty

Tianpei ZU^1,²(), Rui KANG^1,²(), Meilin WEN^1,^2,*()

¹ School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
² Key Laboratory on Reliability and Environmental Engineering Technology, Beijing 100191, China

Received:2019-05-07 Online:2020-06-30 Published:2020-06-30
Contact: Meilin WEN E-mail:zutp93@buaa.edu.cn;kangrui@buaa.edu.cn;wenmeilin@buaa.edu.cn
About author:ZU Tianpei was born in 1993. She is a Ph.D. candidate student on systems engineering at School of Reliability and Systems Engineering, Beihang University. She received her B.S. degree in quality and systems engineering from Beihang University in 2016. Her research focuses on belief reliability, multi-source information fusion, and optimization methods under uncertainty environments. She has published three SCI papers and one EI paper as first author or first student author on optimization under uncertainty environments, and one SCI paper and one EI paper as first author on the method to obtain belief reliability distribution. E-mail: zutp93@buaa.edu.cn|KANG Rui was born in 1966. He is a distinguished professor in School of Reliability and Systems Engineering, Beihang University, Beijing, China. He received his bachelor's and master's degrees in electrical engineering from Beihang University in 1987 and 1990, respectively. He has developed six courses, and published eight books and more than 200 research papers. He is currently serving as the associate editor of IEEE Trans. on Reliability and is the founder of China Prognostics and Health Management Society. He received several awards from the Chinese government for his outstanding scientific contributions, including Changjiang Chair Professor awarded by the Chinese Ministry of Education. His main research interests include reliability, resilience for complex system and modeling epistemic uncertainty in reliability and maintainability. E-mail: kangrui@buaa.edu.cn|WEN Meilin was born in 1980. She received her Ph.D. degree in mathematics from Tsinghua University, Beijing, China, in 2008. She is an associate professor in School of Reliability and Systems Engineering, Beihang University. She has published a monograph on data envelopment analysis and more than 30 papers. Her main research interests include belief reliability theory, uncertainty theory and its applications, data envelopment analysis, and optimization method under uncertain environments. E-mail: wenmeilin@buaa.edu.cn
Supported by:
the National Natural Science Foundation of China(61573043);the National Natural Science Foundation of China(71671009);This work was supported by the National Natural Science Foundation of China (61573043; 71671009)

Abstract

Abstract:

In reliability engineering, the observations of the variables of interest are always limited due to cost or schedule constraints. Consequently, the epistemic uncertainty, which derives from lack of knowledge and information, plays a vital influence on the reliability evaluation. Belief reliability is a new reliability metric that takes the impact of epistemic uncertainty into consideration and belief reliability distribution is fundamental to belief reliability application. This paper develops a new method called graduation formula to construct belief reliability distribution with limited observations. The developed method constructs the belief reliability distribution by determining the corresponding belief degrees of the observations. An algorithm is designed for the graduation formula as it is a set of transcendental equations, which is difficult to determine the analytical solution. The developed method and the proposed algorithm are illustrated by two numerical examples to show their efficiency and future application.

Key words: belief reliability, belief reliability distribution, epistemic uncertainty

Tianpei ZU, Rui KANG, Meilin WEN. Graduation formula: a new method to construct belief reliability distribution under epistemic uncertainty[J]. Journal of Systems Engineering and Electronics, 2020, 31(3): 626-633.

Figures/Tables 4

References 32

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Temperature/K	Sample number
Temperature/K	1$^{\# }$	2$^{\# }$	3$^{\# }$	4$^{\# }$	5$^{\# }$
323	4	3	1	2	5
383	9	10	7	4	5

Data	1	2	3	4	5	4	5	7	9	10
Belief degree	0.023 5	0.134 4	0.500 0	0.865 6	0.976 5	0.027 4	0.084 7	0.500 0	0.915 3	0.972 6

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Graduation formula: a new method to construct belief reliability distribution under epistemic uncertainty

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