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Analysis of minimal cut and path sets based on direct partial Boolean derivatives

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  • Miroslav Kvassay
  • Vitaly Levashenko
  • Elena Zaitseva

Abstract

Principal steps in reliability engineering include estimation of system reliability and identification and quantification of situations which cause a system failure. There are several techniques that can be used to solve these tasks. Some of them are based on minimal cut (path) sets, which represent minimal sets of basic events, whose simultaneous occurrence leads to a failure (repair) of the system. In this article, applications of minimal cut (path) sets in reliability analysis are summarized, and their connection with direct partial Boolean derivatives is studied. In reliability analysis, direct partial Boolean derivatives identify situations in which a failure (repair) of one system component results in a system failure (repair). Therefore, they reveal the influence of one system component on the whole system. However, minimal cut (path) sets define the influence of a simultaneous failure (repair) of a group of system components on the system activity. Therefore, there should be some correlation between direct partial Boolean derivatives and minimal cut (path) sets. This correlation is studied in this article, and as a result, new algorithms for identification of minimal cut (path) sets are proposed based on this correlation.

Suggested Citation

  • Miroslav Kvassay & Vitaly Levashenko & Elena Zaitseva, 2016. "Analysis of minimal cut and path sets based on direct partial Boolean derivatives," Journal of Risk and Reliability, , vol. 230(2), pages 147-161, April.
    • Handle: RePEc:sae:risrel:v:230:y:2016:i:2:p:147-161
    DOI: 10.1177/1748006X15598722
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    References listed on IDEAS

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    1. Schneeweiss, Winfrid G., 2009. "A short Boolean derivation of mean failure frequency for any (also non-coherent) system," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1363-1367.
    2. Barlow, Richard E. & Proschan, Frank, 1975. "Importance of system components and fault tree events," Stochastic Processes and their Applications, Elsevier, vol. 3(2), pages 153-173, April.
    3. Yeh, Wei-Chang, 2006. "A new algorithm for generating minimal cut sets in k-out-of-n networks," Reliability Engineering and System Safety, Elsevier, vol. 91(1), pages 36-43.
    4. Contini, Sergio & Matuzas, Vaidas, 2011. "Analysis of large fault trees based on functional decomposition," Reliability Engineering and System Safety, Elsevier, vol. 96(3), pages 383-390.
    5. Yeh, Wei-Chang, 2008. "An improved algorithm for searching all minimal cuts in modified networks," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 1018-1024.
    6. Haarla, Liisa & Pulkkinen, Urho & Koskinen, Mikko & Jyrinsalo, Jussi, 2008. "A method for analysing the reliability of a transmission grid," Reliability Engineering and System Safety, Elsevier, vol. 93(2), pages 277-287.
    7. Choi, Jong Soo & Cho, Nam Zin, 2007. "A practical method for accurate quantification of large fault trees," Reliability Engineering and System Safety, Elsevier, vol. 92(7), pages 971-982.
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    Cited by:

    1. Kawahara, Jun & Sonoda, Koki & Inoue, Takeru & Kasahara, Shoji, 2019. "Efficient construction of binary decision diagrams for network reliability with imperfect vertices," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 142-154.

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