IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v138y2015icp135-144.html
   My bibliography  Save this article

Importance analysis based on logical differential calculus and Binary Decision Diagram

Author

Listed:
  • Zaitseva, Elena
  • Levashenko, Vitaly
  • Kostolny, Jozef

Abstract

System availability evaluation, sensitivity analysis, Importance Measures, and optimal design are important issues that have become research topics for reliability engineering. There are different mathematical approaches to the development of these topics. The structure function based approach is one of them. Structure function enables one to analyse a system of any complexity. But computational complexity of structure function based methods is time consuming for large-scale networks. We propose to use two mathematical approaches for decision to this problem for system importance analysis. The first of them is Direct Partial Boolean Derivative. New equations for calculating the Importance Measures are developed in terms of these derivatives. The second is Binary Decision Diagram (BDD), that supports efficient manipulation of Boolean algebra. Two algorithms for calculating Direct Partial Boolean Derivative based on BDD of structure function are proposed in this paper. The experimental results show the efficiency of new algorithms for calculating Direct Partial Boolean Derivative and Importance Measures.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:138:y:2015:i:c:p:135-144
    DOI: 10.1016/j.ress.2015.01.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832015000198
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2015.01.009?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. Xing, Liudong & Shrestha, Akhilesh & Dai, Yuanshun, 2011. "Exact combinatorial reliability analysis of dynamic systems with sequence-dependent failures," Reliability Engineering and System Safety, Elsevier, vol. 96(10), pages 1375-1385.
    2. 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.
    3. 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.
    4. Xing, Liudong & Levitin, Gregory, 2013. "BDD-based reliability evaluation of phased-mission systems with internal/external common-cause failures," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 145-153.
    5. 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.
    6. Bjorkman, Kim, 2013. "Solving dynamic flowgraph methodology models using binary decision diagrams," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 206-216.
    7. Li, Shumin & Si, Shubin & Dui, Hongyan & Cai, Zhiqiang & Sun, Shudong, 2014. "A novel decision diagrams extension method," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 107-115.
    8. Gao, Xueli & Cui, Lirong & Li, Jinlin, 2007. "Analysis for joint importance of components in a coherent system," European Journal of Operational Research, Elsevier, vol. 182(1), pages 282-299, October.
    9. Elena Zaitseva, 2012. "Importance Analysis of a Multi-State System Based on Multiple-Valued Logic Methods," Springer Series in Reliability Engineering, in: Anatoly Lisnianski & Ilia Frenkel (ed.), Recent Advances in System Reliability, chapter 0, pages 113-134, Springer.
    10. Duflot, Nicolas & Bérenguer, Christophe & Dieulle, Laurence & Vasseur, Dominique, 2009. "A min cut-set-wise truncation procedure for importance measures computation in probabilistic safety assessment," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1827-1837.
    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. Yeh, Wei-Chang, 2021. "A quick BAT for evaluating the reliability of binary-state networks," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    2. 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.
    3. 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.
    4. 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.
    5. Nicolae Brînzei & Jean-François Aubry, 2018. "Graphs models and algorithms for reliability assessment of coherent and non-coherent systems," Journal of Risk and Reliability, , vol. 232(2), pages 201-215, April.
    6. 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).
    7. Elena Zaitseva & Vitaly Levashenko & Ravil Mukhamediev & Nicolae Brinzei & Andriy Kovalenko & Adilkhan Symagulov, 2023. "Review of Reliability Assessment Methods of Drone Swarm (Fleet) and a New Importance Evaluation Based Method of Drone Swarm Structure Analysis," Mathematics, MDPI, vol. 11(11), pages 1-26, June.

    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. Di Maio, Francesco & Baronchelli, Samuele & Zio, Enrico, 2014. "Hierarchical differential evolution for minimal cut sets identification: Application to nuclear safety systems," European Journal of Operational Research, Elsevier, vol. 238(2), pages 645-652.
    2. Wu, Shaomin & Coolen, Frank P.A., 2013. "A cost-based importance measure for system components: An extension of the Birnbaum importance," European Journal of Operational Research, Elsevier, vol. 225(1), pages 189-195.
    3. Zhai, Qingqing & Yang, Jun & Xie, Min & Zhao, Yu, 2014. "Generalized moment-independent importance measures based on Minkowski distance," European Journal of Operational Research, Elsevier, vol. 239(2), pages 449-455.
    4. Dui, Hongyan & Li, Shumin & Xing, Liudong & Liu, Hanlin, 2019. "System performance-based joint importance analysis guided maintenance for repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 162-175.
    5. 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).
    6. 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.
    7. Dui, Hongyan & Wu, Shaomin & Zhao, Jiangbin, 2021. "Some extensions of the component maintenance priority," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    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. Rocco, Claudio M. & Hernandez-Perdomo, Elvis & Mun, Johnathan, 2021. "Application of logic regression to assess the importance of interactions between components in a network," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    10. 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.
    11. Mo, Yuchang & Xing, Liudong & Amari, Suprasad V. & Bechta Dugan, Joanne, 2015. "Efficient analysis of multi-state k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 95-105.
    12. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    13. 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.
    14. 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.
    15. 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.
    16. 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).
    17. Borgonovo, E. & Smith, C.L., 2012. "Composite multilinearity, epistemic uncertainty and risk achievement worth," European Journal of Operational Research, Elsevier, vol. 222(2), pages 301-311.
    18. Xiaoyan Zhu & Mahmoud Boushaba & Abdelmoumene Boulahia & Xian Zhao, 2019. "A linear m-consecutive-k-out-of-n system with sparse d of non-homogeneous Markov-dependent components," Journal of Risk and Reliability, , vol. 233(3), pages 328-337, June.
    19. 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.
    20. Peng, Rui & Wu, Di & Xiao, Hui & Xing, Liudong & Gao, Kaiye, 2019. "Redundancy versus protection for a non-reparable phased-mission system subject to external impacts," Reliability Engineering and System Safety, Elsevier, vol. 191(C).

    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:138:y:2015:i:c:p:135-144. 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.