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Fuzzy Probability Distributions in Reliability Analysis, Fuzzy HPD-regions, and Fuzzy Predictive Distributions

  • Reinhard ViertlEmail author
  • Shohreh Mirzaei Yeganeh
Chapter
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Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 285)

Abstract

In reliability analysis there are different kinds of uncertainty present: variability, imprecision of lifetimes, model uncertainty concerning probability distributions, and uncertainty of a-priori information in Bayesian analysis. For the description of imprecise lifetimes so-called fuzzy numbers are suitable. In order to model the uncertainty of a-priori information fuzzy probability distributions are the most up-to-date mathematical structure.

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References

  1. 1.
    Möller, B., Beer, M.: Fuzzy Randomness — Uncertainty in Civil Engineering and Computational Mechanics. Springer, Berlin (2004)zbMATHGoogle Scholar
  2. 2.
    Viertl, R.: On reliability estimation based on fuzzy lifetime data. Journal of Statistical Planning and Inference 139, 1750–1755 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Viertl, R.: Statistical Methods for Fuzzy Data. Wiley, Chichester (2011)zbMATHCrossRefGoogle Scholar
  4. 4.
    Viertl, R.: On predictive densities in fuzzy Bayesian inference. In: Faber, M., et al. (eds.) Applications of Statistics and Probability in Civil Engineering. Taylor & Francis, London (2011)Google Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Statistics and Probability TheoryVienna University of TechnologyViennaAustria

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