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A new approach to evaluate reliability of multistate networks under the cost constraint

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  • Yeh, Wei-Chang

Abstract

A multistate network is a system composed of multistate components. The network reliability under the cost constraint for level (d,c) can be computed in terms of (d,c)-MP (MP stands for minimal path) which is a vector such that d units of flow can be transmitted between two specified nodes with the total cost not greater than c. In this study, a new algorithm was developed to evaluate the reliability of multistate networks under cost constraint in terms of the entire (d,c)-MPs. The proposed method is more efficient than the best-known existing algorithm. One example is illustrated to show how all (d,c)-MPs are generated by the proposed algorithm. The reliability of this example is then computed. The computational complexity of the proposed algorithm is also analyzed.

Suggested Citation

  • Yeh, Wei-Chang, 2005. "A new approach to evaluate reliability of multistate networks under the cost constraint," Omega, Elsevier, vol. 33(3), pages 203-209, June.
    • Handle: RePEc:eee:jomega:v:33:y:2005:i:3:p:203-209
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Yi-Kuei Lin & Cheng-Fu Huang, 2016. "Reliability evaluation according to a routing scheme for multi-state computer networks under assured accuracy rate," Annals of Operations Research, Springer, vol. 244(1), pages 221-240, September.
    2. Yi-Kuei Lin & Cheng-Fu Huang, 2013. "Assessing reliability within error rate and time constraint for a stochastic node-imperfect computer network," Journal of Risk and Reliability, , vol. 227(1), pages 80-85, February.
    3. Chin‐Chia Jane & Yih‐Wenn Laih, 2012. "Evaluating cost and reliability integrated performance of stochastic logistics systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(7), pages 577-586, October.
    4. Xu, Xiu-Zhen & Zhou, Run-Hui & Wu, Guo-Lin & Niu, Yi-Feng, 2024. "Evaluating the transmission distance-constrained reliability for a multi-state flow network," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    5. Niu, Yi-Feng & Song, Yi-Fan & Xu, Xiu-Zhen & Zhao, Xia, 2022. "Efficient reliability computation of a multi-state flow network with cost constraint," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    6. Lin, Yi-Kuei & Yeh, Cheng-Ta, 2012. "Determining the optimal double-component assignment for a stochastic computer network," Omega, Elsevier, vol. 40(1), pages 120-130, January.
    7. Lin, Yi-Kuei, 2007. "Performance evaluation for the logistics system in case that capacity weight varies from arcs and types of commodity," International Journal of Production Economics, Elsevier, vol. 107(2), pages 572-580, June.
    8. Xu, Xiu-Zhen & Niu, Yi-Feng & Song, Yi-Fan, 2021. "Computing the reliability of a stochastic distribution network subject to budget constraint," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    9. Cancela, Héctor & Petingi, Louis, 2007. "Properties of a generalized source-to-all-terminal network reliability model with diameter constraints," Omega, Elsevier, vol. 35(6), pages 659-670, December.
    10. Niu, Yi-Feng & Lam, William H.K. & Gao, Ziyou, 2014. "An efficient algorithm for evaluating logistics network reliability subject to distribution cost," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 67(C), pages 175-189.
    11. Yi-Kuei Lin & Chih-Li Pan, 2016. "Data transmission reliability evaluation of a stochastic computer network through minimal paths with a retransmission mechanism," Journal of Risk and Reliability, , vol. 230(6), pages 551-560, December.
    12. Yeh, Wei-Chang, 2007. "An improved sum-of-disjoint-products technique for the symbolic network reliability analysis with known minimal paths," Reliability Engineering and System Safety, Elsevier, vol. 92(2), pages 260-268.
    13. Yeh, Wei-Chang, 2006. "The k-out-of-n acyclic multistate-node networks reliability evaluation using the universal generating function method," Reliability Engineering and System Safety, Elsevier, vol. 91(7), pages 800-808.
    14. 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).
    15. Lin, Yi-Kuei, 2007. "Reliability of a computer network in case capacity weight varying with arcs, nodes and types of commodity," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 646-652.
    16. Yi-Kuei Lin & Thi-Phuong Nguyen & Louis Cheng-Lu Yeng, 2019. "Reliability evaluation of a multi-state air transportation network meeting multiple travel demands," Annals of Operations Research, Springer, vol. 277(1), pages 63-82, June.
    17. Lin, Yi-Kuei, 2010. "A stochastic model to study the system capacity for supply chains in terms of minimal cuts," International Journal of Production Economics, Elsevier, vol. 124(1), pages 181-187, March.

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