Skip to main content

Binary Decision Diagrams for Reliability Studies

  • Chapter
Handbook of Performability Engineering

Abstract

Bryant’s binary ecision diagrams are state-of-the-art data structures used to encode and to manipulate Boolean functions. Risk and dependability studies are heavy consumers of Boolean functions, for the most widely used modeling methods, namely fault trees and event trees, rely on them. The introduction of BDD in that field renewed its algorithmic framework. Moreover, several central mathematical definitions, like the notions of minimal cutsets and importance factors, were questioned. This article attempts to summarize fifteen years of active research on those topics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 429.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 549.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bryant R. Graph based algorithms for boolean function manipulation. IEEE Transactions on Computers 1986; 35(8):677–691.

    Article  MATH  Google Scholar 

  2. Brace K, Rudell R, Bryant R. Efficient implementation of a BDD package. In Proceedings of the 27th ACM/IEEE Design Automation Conference, IEEE 1990; 0738.

    Google Scholar 

  3. Rudell R. Dynamic Variable ordering for ordered binary decision diagrams. In Proceedings of IEEE International Conference on Computer Aided Design, ICCAD 1993; Nov.:42–47.

    Google Scholar 

  4. Bryant R. Symbolic Boolean manipulation with ordered binary decision diagrams. ACM Computing Surveys 1992; Sept. 24:293–318.

    Google Scholar 

  5. Coudert O, Madre J.-C. Fault tree analysis: 1020 prime implicants and beyond. In Proceedings of the Annual Reliability and Maintainability Symposium, ARMS’93, Atlanta NC, USA. 1993; January.

    Google Scholar 

  6. Rauzy A. New algorithms for fault trees analysis. Reliability Engineering and System Safety 1993; 59(2):203–211.

    Article  Google Scholar 

  7. Vesely WE, Goldberg FF, Robert NH, Haasl DF. Fault tree handbook. Technical report NUREG 0492, U.S. Nuclear Regulatory Commission 1981.

    Google Scholar 

  8. Høyland A, Rausand M. System reliability theory. John Wiley & Sons, 1994; ISBN 0-471-59397.

    Google Scholar 

  9. Kumamoto H, Henley EJ. Probabilistic risk assessment and management for engineers and scientists. IEEE Press, 1996; ISBN 0-7803-6017-6.

    Google Scholar 

  10. Minato S.-I. Binary decision diagrams and applications to VLSI CAD. Kluwer, Dordrecht, 1996; ISBN 0-7923-9652-9.

    Google Scholar 

  11. Rauzy A. Mathematical foundation of minimal cutsets. IEEE Transactions on Reliability 2001; 50(4):389–396.

    Article  Google Scholar 

  12. Sinnamon RM, Andrews JD. Improved accuracy in qualitative fault tree analysis. Quality and Reliability Engineering International 1997; 13:285–292.

    Article  Google Scholar 

  13. Sinnamon RM, Andrews JD. Improved efficiency in qualitative fault tree analysis. Quality and Reliability Engineering International 1997; 13:293–298.

    Article  Google Scholar 

  14. Dutuit Y, Rauzy A. Efficient algorithms to assess components and gates importance in fault tree analysis. Reliability Engineering and System Safety 2000; 72(2):213–222.

    Article  Google Scholar 

  15. Epstein S, Rauzy A. Can we trust PRA? Reliability Engineering and System Safety 2005; 88(3):195–205.

    Article  Google Scholar 

  16. Papadimitriou CH. Computational complexity. Addison Wesley, Reading, MA, 1994; ISBN 0-201-53082-1.

    MATH  Google Scholar 

  17. Friedman SJ, Supowit KJ. Finding the optimal variable ordering for binary decision diagrams. IEEE Transactions on Computers 1990; 39(5):710–713.

    Article  MathSciNet  Google Scholar 

  18. Bollig B, Wegener I. Improving the variable ordering of OBDDs is NP-complete. IEEE Trans. on Software Engineering 1996; 45(9):993–1001.

    MATH  Google Scholar 

  19. Aloul FA, Markov IL, Sakallah KA. FORCE: A fast and easy-to-implement variable-ordering heuristic. Proceedings of GLVLSI 2003.

    Google Scholar 

  20. Fujita M, Fujisawa H, Kawato N. Evaluation and improvements of Boolean comparison method based on binary decision diagrams. In Proceedings of IEEE International Conference on Computer Aided Design, ICCAD 1988; 2–5.

    Google Scholar 

  21. Fujita M, Fujisawa H, and Matsugana Y. Variable ordering algorithm for ordered binary decision diagrams and their evaluation. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 1993; 2(1):6–12.

    Article  Google Scholar 

  22. Panda S, Somenzi F. Who are the variables in your neighborhood. In Proceedings of IEEE International Conference on Computer Aided Design, ICCAD 1995; 74–77.

    Google Scholar 

  23. Yau M, Apostolakis G, Guarro S. The use of prime implicants in dependability analysis of software controlled systems. Reliability Engineering and System Safety 1998; 62:23–32.

    Article  Google Scholar 

  24. Morreale E. Recursive operators for prime implicant and irredundant normal form determination. IEEE Transactions on Computers 1970; C-19(6):504–509.

    Article  Google Scholar 

  25. Chandra AK, Markowsky G. On the number of prime implicants. Discrete Mathematics 1978; 24:7–11.

    Article  MATH  MathSciNet  Google Scholar 

  26. Hayase K, Imai H. OBDDs of a monotone function and its prime implicants. Theory of Computing Systems 1998; 41:579–591.

    Article  MathSciNet  Google Scholar 

  27. Jung WS, Han SH, Ha J. A fast BDD algorithm for large coherent fault trees analysis. Reliability Engineering and System Safety 2004; 83:69–374.

    Google Scholar 

  28. Sinnamon RM, Andrews JD. Quantitative fault tree analysis using binary decision diagrams. Journal Européen des Systèmes Automatisés, RAIRO-APII-JESA, Special Issue on Binary Decision Diagrams 1996; 30:1051–1072.

    Google Scholar 

  29. Birnbaum ZW. On the importance of different components and a multicomponent system. In: Korishnaiah PR, editor. Multivariable analysis II. Academic Press, New York, 1969.

    Google Scholar 

  30. Cheok MC, Parry GW, Sherry RR. Use of importance measures in risk informed regulatory applications. Reliability Engineering and System Safety 1998; 60:213–226.

    Article  Google Scholar 

  31. Vesely WE. Supplemental viewpoints on the use of importance measures in risk informed regulatory applications. Reliability Engineering and System Safety 1998; 60:257–259.

    Article  Google Scholar 

  32. Borgonovo E, Apostolakis GE. A new importance measure for risk-informed decision making. Reliability Engineering and System Safety 2001; 72(2):193–212.

    Article  Google Scholar 

  33. Dutuit Y, Rauzy A. Approximate estimation of system reliability via fault trees. Reliability Engineering and System Safety 2005; 87(2):163–172.

    Article  Google Scholar 

  34. Barlow RE, Proschan F. Theory for maintained system: Distribution of time to first failure. Mathematics of Operation Research 1976; 1:32–42.

    Article  MATH  MathSciNet  Google Scholar 

  35. Čepin M. Analysis of truncation limit in probabilistic safety assessment. Reliability Engineering and System Safety 2005; 87(3):395–403.

    Article  Google Scholar 

  36. Jung WS, Han SH. Development of an analytical method to break logical loops at the system level. Reliability Engineering and System Safety 2005; 90(1):37–44.

    Article  MathSciNet  Google Scholar 

  37. Camarinopoulos L, Yllera J. An improved top-down algorithm combined with modularization as highly efficient method for fault tree analysis. Reliability Engineering and System Safety 1985; 11:93–108.

    Google Scholar 

  38. Niemelä I. On simplification of large fault trees. Reliability Engineering and System Safety 1994; 44:135–138.

    Article  Google Scholar 

  39. Chatterjee P. Modularization of fault trees: A method to reduce the cost of analysis. Reliability and Fault Tree Analysis, SIAM 1975; 101–137.

    Google Scholar 

  40. Dutuit Y, Rauzy A. A linear time algorithm to find modules of fault trees. IEEE Transactions on Reliability 1996; 45(3):422–425.

    Article  Google Scholar 

  41. Bouissou M, Bruyère F, Rauzy A. BDD based fault-tree processing: A comparison of variable ordering heuristics. In: Soares C Guedes, editor. Proceedings of European Safety and Reliability Association Conference, ESREL, Pergamon, London, 1997; 3(ISBN 0-08-042835-5):2045–2052.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag London Limited

About this chapter

Cite this chapter

Rauzy, A. (2008). Binary Decision Diagrams for Reliability Studies. In: Misra, K.B. (eds) Handbook of Performability Engineering. Springer, London. https://doi.org/10.1007/978-1-84800-131-2_25

Download citation

  • DOI: https://doi.org/10.1007/978-1-84800-131-2_25

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84800-130-5

  • Online ISBN: 978-1-84800-131-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics