IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v136y2015icp1-7.html
   My bibliography  Save this article

A new cut-based algorithm for the multi-state flow network reliability problem

Author

Listed:
  • Yeh, Wei-Chang
  • Bae, Changseok
  • Huang, Chia-Ling

Abstract

Many real-world systems can be modeled as multi-state network systems in which reliability can be derived in terms of the lower bound points of level d, called d-minimal cuts (d-MCs). This study proposes a new method to find and verify obtained d-MCs with simple and useful found properties for the multi-state flow network reliability problem. The proposed algorithm runs in O(mσp) time, which represents a significant improvement over the previous O(mp2σ) time bound based on max-flow/min-cut, where p, σ and m denote the number of MCs, d-MC candidates and edges, respectively. The proposed algorithm also conquers the weakness of some existing methods, which failed to remove duplicate d-MCs in special cases. A step-by-step example is given to demonstrate how the proposed algorithm locates and verifies all d-MC candidates. As evidence of the utility of the proposed approach, we present extensive computational results on 20 benchmark networks in another example. The computational results compare favorably with a previously developed algorithm in the literature.

Suggested Citation

  • Yeh, Wei-Chang & Bae, Changseok & Huang, Chia-Ling, 2015. "A new cut-based algorithm for the multi-state flow network reliability problem," Reliability Engineering and System Safety, Elsevier, vol. 136(C), pages 1-7.
    • Handle: RePEc:eee:reensy:v:136:y:2015:i:c:p:1-7
    DOI: 10.1016/j.ress.2014.11.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832014002920
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2014.11.010?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. Joseph C. Hudson & Kailash C. Kapur, 1985. "Reliability Bounds for Multistate Systems with Multistate Components," Operations Research, INFORMS, vol. 33(1), pages 153-160, February.
    2. Yan, Zhou & Qian, Meng, 2007. "Improving efficiency of solving d-MC problem in stochastic-flow network," Reliability Engineering and System Safety, Elsevier, vol. 92(1), pages 30-39.
    3. Gregory Levitin, 2005. "The Universal Generating Function in Reliability Analysis and Optimization," Springer Series in Reliability Engineering, Springer, number 978-1-84628-245-4, October.
    Full references (including those not matched with items on IDEAS)

    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. Yeh, Wei-Chang & Tan, Shi-Yi & Zhu, Wenbo & Huang, Chia-Ling & Yang, Guang-yi, 2022. "Novel binary addition tree algorithm (BAT) for calculating the direct lower-bound of the highly reliable binary-state network reliability," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    2. Lin, Yi-Kuei & Huang, Ding-Hsiang, 2020. "Reliability analysis for a hybrid flow shop with due date consideration," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    3. Kozyra, Paweł Marcin, 2023. "The usefulness of (d,b)-MCs and (d,b)-MPs in network reliability evaluation under delivery or maintenance cost constraints," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    4. Zhao, Xian & He, Zongda & Wu, Yaguang & Qiu, Qingan, 2022. "Joint optimization of condition-based performance control and maintenance policies for mission-critical systems," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    5. Hausken, Kjell & Levitin, Gregory, 2009. "Minmax defense strategy for complex multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 577-587.
    6. Lin, Yi-Kuei, 2010. "Calculation of minimal capacity vectors through k minimal paths under budget and time constraints," European Journal of Operational Research, Elsevier, vol. 200(1), pages 160-169, January.
    7. Hindolo George-Williams & Geng Feng & Frank PA Coolen & Michael Beer & Edoardo Patelli, 2019. "Extending the survival signature paradigm to complex systems with non-repairable dependent failures," Journal of Risk and Reliability, , vol. 233(4), pages 505-519, August.
    8. Nourelfath, Mustapha & Ait-Kadi, Daoud, 2007. "Optimization of series–parallel multi-state systems under maintenance policies," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1620-1626.
    9. Bigatti, A.M. & Pascual-Ortigosa, P. & Sáenz-de-Cabezón, E., 2021. "A C++ class for multi-state algebraic reliability computations," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    10. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2024. "Optimal system loading and aborting in additive multi-attempt missions," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    11. Jia, Heping & Ding, Yi & Peng, Rui & Liu, Hanlin & Song, Yonghua, 2020. "Reliability assessment and activation sequence optimization of non-repairable multi-state generation systems considering warm standby," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    12. Lu, Shaoqi & Shi, Daimin & Xiao, Hui, 2019. "Reliability of sliding window systems with two failure modes," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 366-376.
    13. Peng, Rui & Xiao, Hui & Liu, Hanlin, 2017. "Reliability of multi-state systems with a performance sharing group of limited size," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 164-170.
    14. Lin, Yi-Kuei & Yeh, Cheng-Ta, 2011. "Maximal network reliability for a stochastic power transmission network," Reliability Engineering and System Safety, Elsevier, vol. 96(10), pages 1332-1339.
    15. Hu, Yishuang & Ding, Yi & Bao, Minglei, 2024. "An efficient reliability evaluation method for large-scale multi-performance multi-state series-parallel systems considering multi-dimensional approximation," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
    16. Bo, Yimin & Bao, Minglei & Ding, Yi & Hu, Yishuang, 2024. "A DNN-based reliability evaluation method for multi-state series-parallel systems considering semi-Markov process," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    17. Yeh, Wei-Chang, 2017. "Evaluation of the one-to-all-target-subsets reliability of a novel deterioration-effect acyclic multi-state information network," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 132-137.
    18. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2013. "Cold-standby sequencing optimization considering mission cost," Reliability Engineering and System Safety, Elsevier, vol. 118(C), pages 28-34.
    19. Liu, Yu & Chen, Yiming & Jiang, Tao, 2020. "Dynamic selective maintenance optimization for multi-state systems over a finite horizon: A deep reinforcement learning approach," European Journal of Operational Research, Elsevier, vol. 283(1), pages 166-181.
    20. Zio, E. & Bazzo, R., 2011. "Level Diagrams analysis of Pareto Front for multiobjective system redundancy allocation," Reliability Engineering and System Safety, Elsevier, vol. 96(5), pages 569-580.

    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:136:y:2015:i:c:p:1-7. 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.