Computing

, Volume 94, Issue 2–4, pp 313–324

A verified realization of a Dempster–Shafer based fault tree analysis

Article

Abstract

Fault tree analysis is a method to determine the likelihood of a system attaining an undesirable state based on the information about its lower level parts. However, conventional approaches cannot process imprecise or incomplete data. There are a number of ways to solve this problem. In this paper, we will consider the one that is based on the Dempster–Shafer theory. The major advantage of the techniques proposed here is the use of verified methods (in particular, interval analysis) to handle Dempster–Shafer structures in an efficient and consistent way. First, we concentrate on DSI (Dempster–Shafer with intervals), a recently developed tool. It is written in MATLAB and serves as a basis for a new add-on for Dempster–Shafer based fault tree analysis. This new add-on will be described in detail in the second part of our paper. Here, we propagate experts’ statements with uncertainties through fault trees, using mixing based on arithmetic averaging. Furthermore, we introduce an implementation of the interval scale based algorithm for estimating system reliability, extended by new input distributions.

Keywords

Dempster–Shafer theory Fault tree analysis MATLAB INTLAB Interval analysis 

Mathematics Subject Classification (2000)

65G30 60A99 

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References

  1. 1.
    Arnold D (2011) Computer arithmetic tragedies. http://www.ima.umn.edu/~arnold/455.f96/disasters.html
  2. 2.
    Auer E, Luther W, Rebner G, Limbourg P (2010) A verified MATLAB toolbox for the Dempster-Shafer theory. In: Proceedings of the workshop on the theory of belief functions. http://www.udue.de/DSIPaperone, http://www.udue.de/DSI
  3. 3.
    Carreras C, Walker I (2001) Interval methods for fault-tree analyses in robotics. IEEE Trans Reliab 50:3–11. http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=00935010 Google Scholar
  4. 4.
    Cheng Y (2000) Uncertainties in fault tree analysis. http://www2.tku.edu.tw/~tkjse/3-1/3-1-3.pdf
  5. 5.
    Ferson S (2002) RAMAS Risk Calc 4.0 software: risk assessment with uncertain numbers. Lewis Publishers, Boca RatonGoogle Scholar
  6. 6.
    Ferson S, Kreinovich V, Ginzburg L, Myers D, Sentz K (2003) Constructing probability boxes and Dempster–Shafer structures. SAND2002-4015. Sandia National Laboratories, WashingtonCrossRefGoogle Scholar
  7. 7.
    Gradstein I, Ryshik I (1981) Summen, Produkt- und Integraltafeln. Harri Deutsch, GermanyGoogle Scholar
  8. 8.
    Guth M (1991) A probability foundation for vagueness and imprecision in fault tree analysis. IEEE Trans Reliab 1(40): 563–570CrossRefGoogle Scholar
  9. 9.
    IEEE Standard for Floating-Point Arithmetic (2008) IEEE Std 754-2008, pp 1–58. doi:10.1109/IEEESTD.2008.4610935
  10. 10.
    Limbourg P (2011) Imprecise probability propagation toolbox (IPP toolbox). http://www.uni-due.de/il/ipptoolbox.php
  11. 11.
    Luther W, Dyllong E, Fausten D, Otten W, Traczinski H (2001) Numerical verification and validation of kinematics and dynamical models for flexible robots in complex environments. In: Perspectives on enclosure methods. Springer, Wien, pp 181–200Google Scholar
  12. 12.
    Martin A (2009) Implementing general belief function framework with a practical codification for low complexity. In: Smarandache F, Dezert J (eds) Advances and applications of DSmT for information fusion. Collected works, vol 3. American Research Press, Rehoboth, pp 217–273Google Scholar
  13. 13.
  14. 14.
    Moore R, Kearfott B, Cloud M (2009) Introduction to interval analysis. Society for Industrial and Applied Mathematics, PhiladelphiaMATHCrossRefGoogle Scholar
  15. 15.
    Rump S (1999) INTLAB–INTerval LABoratory. Dev Reliab Comput 1:77–104. http://www.ti3.tu-harburg.de/
  16. 16.
    Shafer G (1976) A mathematical theory of evidence. Princeton University Press, PrincetonMATHGoogle Scholar
  17. 17.
    Tonon F (2004) Using random set theory to propagate epistemic uncertainty through a mechanical system. Reliab Eng Syst Saf 85(1–3): 169–181CrossRefGoogle Scholar
  18. 18.
    Traczinski H (2006) Integration von Algorithmen und Datentypen zur validierten Mehrkörpersimulation in MOBILE. Dissertation, Universität Duisburg-Essen. Logos-Verlag, Berlin. ISBN 978-3-8325-1457-0Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.University of Duisburg-EssenDuisburgGermany

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