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On the Boolean extension of the Birnbaum importance to non-coherent systems

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  • Aliee, Hananeh
  • Borgonovo, Emanuele
  • Glaß, Michael
  • Teich, Jürgen

Abstract

The Birnbaum importance measure plays a central role in reliability analysis. It has initially been introduced for coherent systems, where several of its properties hold and where its computation is straightforward. This work introduces a Boolean expression for the notion of criticality that allows the seamless extension of the Birnbaum importance to non-coherent systems. As a key feature, the novel definition makes the computation and encoding straightforward with well-established techniques such as Binary Decision Diagrams (BDDs) or Fault Trees (FTs). Several examples and a case study illustrate the findings.

Suggested Citation

  • Aliee, Hananeh & Borgonovo, Emanuele & Glaß, Michael & Teich, Jürgen, 2017. "On the Boolean extension of the Birnbaum importance to non-coherent systems," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 191-200.
    • Handle: RePEc:eee:reensy:v:160:y:2017:i:c:p:191-200
    DOI: 10.1016/j.ress.2016.12.013
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    References listed on IDEAS

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    Cited by:

    1. Zhu, Xiaoyan & Chen, Zhiqiang & Borgonovo, Emanuele, 2021. "Remaining-useful-lifetime and system-remaining-profit based importance measures for decisions on preventive maintenance," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    2. Yang, Liu & Rauzy, Antoine, 2019. "Model synthesis using boolean expression diagrams," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 78-87.
    3. Sedlacek, Peter & Zaitseva, Elena & Levashenko, Vitaly & Kvassay, Miroslav, 2021. "Critical state of non-coherent multi-state system," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    4. Sudhanshu Aggarwal, 2021. "Minimal path set importance in complex systems," Journal of Risk and Reliability, , vol. 235(2), pages 201-208, April.
    5. Rusnak, Patrik & Zaitseva, Elena & Levashenko, Vitaly & Bolvashenkov, Igor & Kammermann, Jörg, 2024. "Importance analysis of a system based on survival signature by structural importance measures," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    6. Fu, Yuqiang & Yuan, Tao & Zhu, Xiaoyan, 2019. "Importance-measure based methods for component reassignment problem of degrading components," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    7. Lyu, Dong & Si, Shubin, 2020. "Dynamic importance measure for the K-out-of-n: G system under repeated random load," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    8. Zaitseva, Elena & Levashenko, Vitaly & Sedlacek, Peter & Kvassay, Miroslav & Rabcan, Jan, 2021. "Logical differential calculus for calculation of Birnbaum importance of non-coherent system," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    9. Lyu, Dong & Si, Shubin, 2021. "Importance measure for K-out-of-n: G systems under dynamic random load considering strength degradation," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    10. Ma, Chengye & Du, Yongjun & Zhang, Yuchun & Cai, Zhiqiang, 2022. "Marginal and joint failure importance for K-terminal network edges under counting process," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    11. Xianzhen Huang & Frank PA Coolen, 2018. "Reliability sensitivity analysis of coherent systems based on survival signature," Journal of Risk and Reliability, , vol. 232(6), pages 627-634, December.
    12. Dui, Hongyan & Wu, Shaomin & Zhao, Jiangbin, 2021. "Some extensions of the component maintenance priority," Reliability Engineering and System Safety, Elsevier, vol. 214(C).

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