IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v160y2017icp191-200.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832016310286
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2016.12.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Vaurio, Jussi K., 2010. "Ideas and developments in importance measures and fault-tree techniques for reliability and risk analysis," Reliability Engineering and System Safety, Elsevier, vol. 95(2), pages 99-107.
    2. D R Prescott & R Remenyte-Prescott & S Reed & J D Andrews & C G Downes, 2009. "A reliability analysis method using binary decision diagrams in phased mission planning," Journal of Risk and Reliability, , vol. 223(2), pages 133-143, June.
    3. Borgonovo, E., 2010. "The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions," European Journal of Operational Research, Elsevier, vol. 204(3), pages 485-495, August.
    4. Vaurio, Jussi K., 2011. "Importance measures in risk-informed decision making: Ranking, optimisation and configuration control," Reliability Engineering and System Safety, Elsevier, vol. 96(11), pages 1426-1436.
    5. R Remenyte-Prescott & J Andrews, 2008. "Analysis of non-coherent fault trees using ternary decision diagrams," Journal of Risk and Reliability, , vol. 222(2), pages 127-138, June.
    6. Vaurio, J.K., 2011. "Importance measures for multi-phase missions," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 230-235.
    7. 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.
    8. Vaurio, Jussi K., 2016. "Importances of components and events in non-coherent systems and risk models," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 117-122.
    9. Emanuele Borgonovo, 2008. "Sensitivity Analysis of Model Output with Input Constraints: A Generalized Rationale for Local Methods," Risk Analysis, John Wiley & Sons, vol. 28(3), pages 667-680, June.
    10. Dutuit, Yves & Rauzy, Antoine, 2015. "On the extension of Importance Measures to complex components," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 161-168.
    11. Zaitseva, Elena & Levashenko, Vitaly & Kostolny, Jozef, 2015. "Importance analysis based on logical differential calculus and Binary Decision Diagram," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 135-144.
    12. J D Andrews, 2008. "A ternary decision diagram method to calculate the component contributions to the failure of systems undergoing phased missions," Journal of Risk and Reliability, , vol. 222(2), pages 173-187, June.
    13. Borgonovo, Emanuele & Aliee, Hananeh & Glaß, Michael & Teich, Jürgen, 2016. "A new time-independent reliability importance measure," European Journal of Operational Research, Elsevier, vol. 254(2), pages 427-442.
    14. Borgonovo, E., 2007. "Differential, criticality and Birnbaum importance measures: An application to basic event, groups and SSCs in event trees and binary decision diagrams," Reliability Engineering and System Safety, Elsevier, vol. 92(10), pages 1458-1467.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dui, Hongyan & Si, Shubin & Wu, Shaomin & Yam, Richard C.M., 2017. "An importance measure for multistate systems with external factors," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 49-57.
    2. Dui, Hongyan & Wu, Shaomin & Zhao, Jiangbin, 2021. "Some extensions of the component maintenance priority," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    3. Vaurio, Jussi K., 2016. "Importances of components and events in non-coherent systems and risk models," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 117-122.
    4. 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).
    5. Dutuit, Yves & Rauzy, Antoine, 2015. "On the extension of Importance Measures to complex components," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 161-168.
    6. 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.
    7. Xiaoyan Zhu & Way Kuo, 2014. "Importance measures in reliability and mathematical programming," Annals of Operations Research, Springer, vol. 212(1), pages 241-267, January.
    8. Borgonovo, Emanuele & Aliee, Hananeh & Glaß, Michael & Teich, Jürgen, 2016. "A new time-independent reliability importance measure," European Journal of Operational Research, Elsevier, vol. 254(2), pages 427-442.
    9. Wu, Shaomin & Chen, Yi & Wu, Qingtai & Wang, Zhonglai, 2016. "Linking component importance to optimisation of preventive maintenance policy," Reliability Engineering and System Safety, Elsevier, vol. 146(C), pages 26-32.
    10. Roy Cerqueti, 2022. "A new concept of reliability system and applications in finance," Annals of Operations Research, Springer, vol. 312(1), pages 45-64, May.
    11. 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).
    12. 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).
    13. 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).
    14. Nguyen, Kim-Anh & Do, Phuc & Grall, Antoine, 2017. "Joint predictive maintenance and inventory strategy for multi-component systems using Birnbaum’s structural importance," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 249-261.
    15. 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).
    16. Jintao Liu & Keping Li & Wei Zheng & Jiebei Zhu, 2019. "An importance order analysis method for causes of railway signaling system hazards based on complex networks," Journal of Risk and Reliability, , vol. 233(4), pages 567-579, August.
    17. Emanuele Borgonovo & Alessandra Cillo & Curtis L. Smith, 2018. "On the Relationship between Safety and Decision Significance," Risk Analysis, John Wiley & Sons, vol. 38(8), pages 1541-1558, August.
    18. Sudhanshu Aggarwal, 2021. "Minimal path set importance in complex systems," Journal of Risk and Reliability, , vol. 235(2), pages 201-208, April.
    19. Dui, Hongyan & Si, Shubin & Yam, Richard C.M., 2018. "Importance measures for optimal structure in linear consecutive-k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 339-350.
    20. Zhu, Xiaoyan & Fu, Yuqiang & Yuan, Tao & Wu, Xinying, 2017. "Birnbaum importance based heuristics for multi-type component assignment problems," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 209-221.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:160:y:2017:i:c:p:191-200. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.