Skip to main content
SpringerLink
Log in
Book cover

Probabilistic Safety Assessment and Management pp 2872–2880Cite as

A Method for Finding Prime Implicants in Incoherent Fault Trees by Use of Commonly Available Tools for Minimal Cut Set Analysis in Coherent Fault Trees

  • Conference paper

  • 26 Accesses

Abstract

This paper outlines a method to find the prime implicants of incoherent fault trees using a fault tree transformation and commonly available tools for the analysis of minimal cut sets of coherent fault trees, and by post processing the results.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Veitch, E. W. (1952), A chart method for simplifying truth functions, May 1952 in Proc. Assoc. for Computing Machinery, Pittsburgh.

    Google Scholar 

  2. Karnaugh, M. (1953), The map method for synthesis of combinational logic circuit, Nov 1953 in Trans. AIEE Communications and Electronics. 72, S.593–599

    MathSciNet  Google Scholar 

  3. McCluskey, E. J. (1956), Minimisation of boolean Functions, 1956 in Bell System technical Journal. S. 1417–1444

    Google Scholar 

  4. Quine, W. V. O. (1959), On cores and prime implicants of truth functions, Nov. 1959 in American Mathematical Monthly 66: No. 9, S.755–760 Lancaster PA., ISSN 0002-9890

    Article  MATH  MathSciNet  Google Scholar 

  5. Chandra, A., Markowsky, G. (1978), On the number of prime implicants. Discrete Mathematics 24: 7–11 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  6. Garey, M., Johnson, D. (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, San Francisco

    MATH  Google Scholar 

  7. Bryant, R. E. (1982), Symbolic Boolean Manipulation with Ordered Binary Decision Diagrams, ACM Computing Surveys, Vol. 24, No. 3 (September, 1992), pp. 293–318.

    Article  Google Scholar 

  8. Sedgewick, R. (1992), Algorithms in C++, Addison-Wesley, Reading MA (1992)

    Google Scholar 

  9. Contini, S., de Cola, G. (1996), A Top Down Approach to Fault Tree Analysis Using Binary Decision Diagrams, European Journal of Automation, 30(8), 1996

    Google Scholar 

  10. Hayase, K., Imai, H. (1998), OBDDs of a Monotone Function and Its Prime Implicants, Theory Comput. Systems 31: 579–591 (1998) by Springer-Verlag New York

    Article  MATH  MathSciNet  Google Scholar 

  11. Hayes, B. (1997), Computing Science Can’t Get No Satisfaction, American Scientist the magazine of Sigma X, Vol. 85, No.2 (March-April, 1997), pp. 108–112

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Gesellschaft für Anlagen-und Reaktorsicherheit (GRS) mbH, Garching, Germany

    Peter Puhr-Westerheide

Authors
  1. Peter Puhr-Westerheide
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. TÜV Süddeutschland, Dudenstrasse 28, D-68167, Mannheim, Germany

    Cornelia Spitzer Dipl.-Math.

  2. Swiss Federal Nuclear Safety Inspectorate (HSK), CH-5232, Villigen-HSK, Switzerland

    Ulrich Schmocker PhD

  3. Paul Scherrer Institut (PSI), CH-5232, Villigen PSI, Switzerland

    Vinh N. Dang PhD

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag London

About this paper

Cite this paper

Puhr-Westerheide, P. (2004). A Method for Finding Prime Implicants in Incoherent Fault Trees by Use of Commonly Available Tools for Minimal Cut Set Analysis in Coherent Fault Trees. In: Spitzer, C., Schmocker, U., Dang, V.N. (eds) Probabilistic Safety Assessment and Management. Springer, London. https://doi.org/10.1007/978-0-85729-410-4_460

Download citation

  • DOI: https://doi.org/10.1007/978-0-85729-410-4_460

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-1057-6

  • Online ISBN: 978-0-85729-410-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation