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Linear multistate consecutively-connected systems subject to a constrained number of gaps

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  • Levitin, Gregory
  • Xing, Liudong
  • Dai, Yuanshun

Abstract

Linear multistate consecutively-connected systems (LMCCS) are systems that consist of a set of linearly ordered nodes with some of them containing statistically independent multistate connection elements (MCEs). Each MCE can provide a connection between its host node and a random number of next nodes along the sequence based on a known probability mass function. In traditional LMCCS models, the disconnection of any node causes the failure of the entire system. These models are too strict and thus not appropriate for some real-world applications such as those in sensor detection systems and flow transfer systems, which can tolerate a certain number of disconnected nodes referred to as gaps. In this work, we generalize the traditional LMCCS models by introducing a limited number of allowable gaps. The system fails if the number of gaps exceeds a specified limit. To analyze the reliability of the generalized LMCCS subject to a constrained total number of gaps, a universal generating function based method is first suggested. An optimal element sequencing problem is then solved considering that the system reliability can strongly depend on the sequence of different MCEs along the line. Examples are provided to demonstrate the proposed methodology.

Suggested Citation

  • Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2015. "Linear multistate consecutively-connected systems subject to a constrained number of gaps," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 246-252.
    • Handle: RePEc:eee:reensy:v:133:y:2015:i:c:p:246-252
    DOI: 10.1016/j.ress.2014.09.004
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    References listed on IDEAS

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    1. Levitin, Gregory, 2003. "Optimal allocation of multi-state elements in linear consecutively connected systems with vulnerable nodes," European Journal of Operational Research, Elsevier, vol. 150(2), pages 406-419, October.
    2. Gregory Levitin, 2005. "The Universal Generating Function in Reliability Analysis and Optimization," Springer Series in Reliability Engineering, Springer, number 978-1-84628-245-4, December.
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    Cited by:

    1. Xing, Liudong & Levitin, Gregory, 2018. "Connectivity modeling and optimization of linear consecutively connected systems with repairable connecting elements," European Journal of Operational Research, Elsevier, vol. 264(2), pages 732-741.
    2. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2024. "Consecutively connected systems with unreliable resource generators and storages," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    3. Patricia Pascual-Ortigosa & Eduardo Sáenz-de-Cabezón, 2021. "Algebraic Analysis of Variants of Multi-State k -out-of- n Systems," Mathematics, MDPI, vol. 9(17), pages 1-15, August.
    4. Ji Hwan Cha & Maxim Finkelstein, 2019. "On some characteristics of quality for systems operating in a random environment," Journal of Risk and Reliability, , vol. 233(2), pages 257-267, April.
    5. Yi, He & Cui, Lirong, 2017. "Distribution and availability for aggregated second-order semi-Markov ternary system with working time omission," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 50-60.
    6. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2017. "Optimal arrangement of connecting elements in linear consecutively connected systems with heterogeneous warm standby groups," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 395-401.
    7. Yu, Huan & Yang, Jun & Peng, Rui & Zhao, Yu, 2016. "Reliability evaluation of linear multi-state consecutively-connected systems constrained by m consecutive and n total gaps," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 35-43.
    8. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2018. "Connectivity evaluation and optimal service centers allocation in repairable linear consecutively connected systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 187-193.
    9. Ji Hwan Cha & Maxim Finkelstein, 2019. "Optimal preventive maintenance for systems having a continuous output and operating in a random environment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 327-350, July.
    10. Dui, Hongyan & Tian, Tianzi & Zhao, Jiangbin & Wu, Shaomin, 2022. "Comparing with the joint importance under consideration of consecutive-k-out-of-n system structure changes," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    11. Ji Hwan Cha & Maxim Finkelstein, 2020. "Stochastic modelling of operational quality of k-out-of-n systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 424-441, July.
    12. Jinlei Qin & Zheng Li, 2019. "Reliability and Sensitivity Analysis Method for a Multistate System with Common Cause Failure," Complexity, Hindawi, vol. 2019, pages 1-8, May.

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