Fuzzy Optimization and Decision Making

, Volume 12, Issue 1, pp 15–27 | Cite as

Belief reliability: a new metrics for products’ reliability

  • Zhiguo Zeng
  • Meilin Wen
  • Rui Kang


Traditional reliability metrics are based on probability measures. However, in engineering practices, failure data are often so scarce that traditional metrics cannot be obtained. Furthermore, in many applications, premises of applying these metrics are violated frequently. Thus, this paper will give some new reliability metrics which can evaluate products’ reliability with few failure data. Firstly, the new metrics are defined based on uncertainty theory and then, numerical evaluation methods for them are presented. Furthermore, a numerical algorithm based on the fault tree is developed in order to evaluate systems’ reliability in the context of defined metrics. Finally, the proposed metrics and evaluation methods are illustrated with some case studies.


Uncertainty theory Reliability Fault tree 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Cai K., Wen C., Zhang M. (1991) Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context. Fuzzy Sets And Systems 42(2): 145–172MathSciNetMATHCrossRefGoogle Scholar
  2. Chen X., Liu B. (2010) Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optimization and Decision Making 9(1): 69–81MathSciNetMATHCrossRefGoogle Scholar
  3. Ebeling C. (2010) An introduction to reliability and maintainability engineering. Waveland Press, Long GroveGoogle Scholar
  4. Fussell J., Vesely W. (1972) New methodology for obtaining cut sets for fault trees. Transactions of American Nuclear Society 15(1): 262–269Google Scholar
  5. Liu B. (2007) Uncertainty theory (2nd ed.). Springer, BerlinMATHGoogle Scholar
  6. Liu B. (2009) Some research problems in uncertainty theory. Journal of Uncertain Systems 3(1): 3–10Google Scholar
  7. Liu B. (2010) Uncertain risk analysis and uncertain reliability analysis. Journal of Uncertain Systems 4(3): 163–170Google Scholar
  8. Liu B. (2011) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, BerlinGoogle Scholar
  9. Liu B. (2012) Why is there a need for uncertainty theory?. Journal of Uncertain Systems 6(1): 3–10Google Scholar
  10. Meeker W., Escobar L. (1998) Statistical methods for reliability data. Wiley, New YorkMATHGoogle Scholar
  11. Meeker W., Hamada M. (1995) Statistical tools for the rapid development and evaluation of high-reliability products. IEEE Transactions on Reliability 44(2): 187–198CrossRefGoogle Scholar
  12. Nelson W. (1990) Accelerated testing: statistical models, test plans and data analyses. Wiley, New YorkGoogle Scholar
  13. Peng Z., Iwamura K. (2010) A sufficient and necessary condition of uncertainty distribution. Journal of Interdisciplinary Mathematics 3(1): 277–285MathSciNetGoogle Scholar
  14. Tan M., Tang X. (2006) The further study of safety stock under uncertain environment. Fuzzy Optimization and Decision Making 5(2): 193–202MATHCrossRefGoogle Scholar
  15. Tversky A., Kahneman D. (1986) Rational choice and the framing of decisions. Journal of Business 59: 251–278CrossRefGoogle Scholar
  16. Wang, Z. (2010). Structural reliability analysis using uncertainty theory. In Proceedings of the first international conference on uncertainty theory (pp. 166–170), Urumchi.Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.School of Reliability and Systems EngineeringBeihang UniversityBeijingChina
  2. 2.State Key Laboratory of Virtual Reality Technology and Systems and School of Reliability and Systems EngineeringBeihang UniversityBeijingChina

Personalised recommendations