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On Birnbaum importance assessment for aging multi-state system under minimal repair by using the Lz-transform method

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  • Lisnianski, Anatoly
  • Frenkel, Ilia
  • Khvatskin, Lev

Abstract

This paper considers a reliability importance evaluation for components in an aging multi-state system. In practical reliability engineering a “curse of dimensionality†(the large number of states that should be analyzed for a multi-state system model) is a main obstacle for importance assessment. In order to challenge the problem, this paper proposes a new method that is based on an LZ-transform of the discrete-state continuous-time Markov process and on Ushakov׳s Universal Generating Operator. The paper shows that the proposed method can drastically reduce a computational burden. In order to illustrate the method, a solution of a real world problem is presented as a numerical example.

Suggested Citation

  • Lisnianski, Anatoly & Frenkel, Ilia & Khvatskin, Lev, 2015. "On Birnbaum importance assessment for aging multi-state system under minimal repair by using the Lz-transform method," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 258-266.
    • Handle: RePEc:eee:reensy:v:142:y:2015:i:c:p:258-266
    DOI: 10.1016/j.ress.2015.05.006
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    References listed on IDEAS

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    1. Huseby, Arne B. & Natvig, Bent, 2013. "Discrete event simulation methods applied to advanced importance measures of repairable components in multistate network flow systems," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 186-198.
    2. 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.
    3. Lisnianski, Anatoly & Ding, Yi, 2009. "Redundancy analysis for repairable multi-state system by using combined stochastic processes methods and universal generating function technique," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1788-1795.
    4. Bent Natvig, 2011. "Measures of Component Importance in Nonrepairable and Repairable Multistate Strongly Coherent Systems," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 523-547, September.
    5. Gregory Levitin, 2005. "The Universal Generating Function in Reliability Analysis and Optimization," Springer Series in Reliability Engineering, Springer, number 978-1-84628-245-4, February.
    6. Natvig, Bent, 1979. "A suggestion of a new measure of importance of system components," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 319-330, December.
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    Cited by:

    1. Liu, Yu & Chen, Yiming & Jiang, Tao, 2018. "On sequence planning for selective maintenance of multi-state systems under stochastic maintenance durations," European Journal of Operational Research, Elsevier, vol. 268(1), pages 113-127.
    2. Lisnianski, Anatoly & Levit, Evgeniy & Teper, Lina, 2021. "Short-term availability and performability analysis for a large-scale multi-state system based on robotic sensors," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    3. 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.
    4. Cai, Zhiqiang & Si, Shubin & Sun, Shudong & Li, Caitao, 2016. "Optimization of linear consecutive-k-out-of-n system with a Birnbaum importance-based genetic algorithm," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 248-258.
    5. Wu, Bei & Cui, Lirong & Fang, Chen, 2020. "Multi-state balanced systems with multiple failure criteria," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    6. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2017. "Optimal loading of series parallel systems with arbitrary element time-to-failure and time-to-repair distributions," Reliability Engineering and System Safety, Elsevier, vol. 164(C), pages 34-44.
    7. Vaisman, Radislav & Sun, Yuting, 2021. "Reliability and importance measure analysis of networks with shared risk link groups," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    8. 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.

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