IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v221y2012i1p138-147.html
   My bibliography  Save this article

Reliability and covariance estimation of weighted k-out-of-n multi-state systems

Author

Listed:
  • Wang, Yong
  • Li, Lin
  • Huang, Shuhong
  • Chang, Qing

Abstract

In the literature of reliability engineering, reliability of the weighted k-out-of-n system can be calculated using component reliability based on the structure function. The calculation usually assumes that the true component reliability is completely known. However, this is not the case in practical applications. Instead, component reliability has to be estimated using empirical sample data. Uncertainty arises during this estimation process and propagates to the system level. This paper studies the propagation mechanism of estimation uncertainty through the universal generating function method. Equations of the complete solution including the unbiased system reliability estimator and the corresponding unbiased covariance estimator are derived. This is a unified approach. It can be applied to weighted k-out-of-n systems with multi-state components, to weighted k-out-of-n systems with binary components, and to simple series and parallel systems. It may also serve as building blocks to derive estimators of system reliability and uncertainty measures for more complicated systems.

Suggested Citation

  • Wang, Yong & Li, Lin & Huang, Shuhong & Chang, Qing, 2012. "Reliability and covariance estimation of weighted k-out-of-n multi-state systems," European Journal of Operational Research, Elsevier, vol. 221(1), pages 138-147.
    • Handle: RePEc:eee:ejores:v:221:y:2012:i:1:p:138-147
    DOI: 10.1016/j.ejor.2012.02.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712001877
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2012.02.037?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. Levitin, Gregory & Xie, Min & Zhang, Tieling, 2007. "Reliability of fault-tolerant systems with parallel task processing," European Journal of Operational Research, Elsevier, vol. 177(1), pages 420-430, February.
    2. Li, Wei & Zuo, Ming J., 2008. "Reliability evaluation of multi-state weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 160-167.
    3. Ramírez-Márquez, José E. & Jiang, Wei, 2006. "Confidence bounds for the reliability of binary capacitated two-terminal networks," Reliability Engineering and System Safety, Elsevier, vol. 91(8), pages 905-914.
    4. 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.
    5. Long, Q. & Xie, M. & Ng, S.H. & Levitin, Gregory, 2008. "Reliability analysis and optimization of weighted voting systems with continuous states input," European Journal of Operational Research, Elsevier, vol. 191(1), pages 240-252, November.
    6. Ushakov, Igor, 2000. "The method of generalized generating sequences," European Journal of Operational Research, Elsevier, vol. 125(2), pages 316-323, September.
    7. Jane, Chin-Chia & Laih, Yih-Wenn, 2010. "A dynamic bounding algorithm for approximating multi-state two-terminal reliability," European Journal of Operational Research, Elsevier, vol. 205(3), pages 625-637, September.
    8. Zhigang Tian & Wei Li & Ming J. Zuo, 2008. "Modeling and Reliability Evaluation of Multi-state k-out-of-n Systems," Springer Series in Reliability Engineering, in: Hoang Pham (ed.), Recent Advances in Reliability and Quality in Design, chapter 2, pages 31-56, Springer.
    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. Jorgen Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2021. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Papers 2112.10672, arXiv.org.
    2. Aboalkhair, Ahmad M. & Coolen, Frank P.A. & MacPhee, Iain M., 2013. "Nonparametric predictive reliability of series of voting systems," European Journal of Operational Research, Elsevier, vol. 226(1), pages 77-84.
    3. Serkan Eryilmaz & Ali Riza Bozbulut, 2019. "Reliability analysis of weighted- k -out-of- n system consisting of three-state components," Journal of Risk and Reliability, , vol. 233(6), pages 972-977, December.
    4. Xiaojun Liang & Yinghui Tang, 2019. "The improvement upon the reliability of the k-out-of-n:F system with the repair rates differentiation policy," Operational Research, Springer, vol. 19(2), pages 479-500, June.
    5. Nizar Mannai & Soufiane Gasmi, 2020. "Optimal design of k-out-of-n system under first and last replacement in reliability theory," Operational Research, Springer, vol. 20(3), pages 1353-1368, September.
    6. Qianru Ge & Willem van Jaarsveld & Zümbül Atan, 2020. "Optimal redesign decisions through failure rate estimates," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(4), pages 254-271, June.
    7. Jing Li & Guodong Wang & Haofei Zhou & Honggen Chen, 2023. "Redundancy allocation optimization for multi-state system with hierarchical performance requirements," Journal of Risk and Reliability, , vol. 237(6), pages 1031-1047, December.
    8. Jørgen Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03634370, HAL.
    9. Eryilmaz, Serkan, 2015. "Capacity loss and residual capacity in weighted k-out-of-n:G systems," Reliability Engineering and System Safety, Elsevier, vol. 136(C), pages 140-144.
    10. Faghih-Roohi, Shahrzad & Xie, Min & Ng, Kien Ming & Yam, Richard C.M., 2014. "Dynamic availability assessment and optimal component design of multi-state weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 57-62.
    11. Jørgen Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Post-Print hal-03634370, HAL.
    12. Jørgen Vitting Andersen & Roy Cerqueti & Giulia Rotundo, 2017. "Rational expectations and stochastic systems," Documents de travail du Centre d'Economie de la Sorbonne 17060, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2019.
    13. 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.
    14. Serkan Eryilmaz & Kadir Sarikaya, 2014. "Modeling and analysis of weighted-k-out-of-n: G system consisting of two different types of components," Journal of Risk and Reliability, , vol. 228(3), pages 265-271, June.
    15. Zhang, Nan & Fouladirad, Mitra & Barros, Anne, 2019. "Reliability-based measures and prognostic analysis of a K-out-of-N system in a random environment," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1120-1131.
    16. Fernández, Arturo J., 2015. "Optimum attributes component test plans for k-out-of-n:F Weibull systems using prior information," European Journal of Operational Research, Elsevier, vol. 240(3), pages 688-696.
    17. Jorgen-Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Annals of Operations Research, Springer, vol. 326(1), pages 295-316, July.
    18. Yonit Barron, 2018. "Group maintenance policies for an R-out-of-N system with phase-type distribution," Annals of Operations Research, Springer, vol. 261(1), pages 79-105, February.

    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. 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. Shao, Changzheng & Ding, Yi, 2020. "Two-interdependent-performance multi-state system: Definitions and reliability evaluation," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    3. Chen, Yiming & Liu, Yu & Jiang, Tao, 2021. "Optimal maintenance strategy for multi-state systems with single maintenance capacity and arbitrarily distributed maintenance time," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    4. Li, Yan-Fu & Zio, Enrico, 2012. "A multi-state model for the reliability assessment of a distributed generation system via universal generating function," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 28-36.
    5. Pourkarim Guilani, Pedram & Sharifi, Mani & Niaki, S.T.A. & Zaretalab, Arash, 2014. "Reliability evaluation of non-reparable three-state systems using Markov model and its comparison with the UGF and the recursive methods," Reliability Engineering and System Safety, Elsevier, vol. 129(C), pages 29-35.
    6. 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.
    7. 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.
    8. Jiang, Tao & Liu, Yu, 2017. "Parameter inference for non-repairable multi-state system reliability models by multi-level observation sequences," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 3-15.
    9. Lai, Chyh-Ming & Yeh, Wei-Chang, 2016. "Two-stage simplified swarm optimization for the redundancy allocation problem in a multi-state bridge system," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 148-158.
    10. Long, Q. & Xie, M. & Ng, S.H. & Levitin, Gregory, 2008. "Reliability analysis and optimization of weighted voting systems with continuous states input," European Journal of Operational Research, Elsevier, vol. 191(1), pages 240-252, November.
    11. Liu, Yu & Liu, Qinzhen & Xie, Chaoyang & Wei, Fayuan, 2019. "Reliability assessment for multi-state systems with state transition dependency," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 276-288.
    12. Faghih-Roohi, Shahrzad & Xie, Min & Ng, Kien Ming & Yam, Richard C.M., 2014. "Dynamic availability assessment and optimal component design of multi-state weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 57-62.
    13. Chunyan, Ling & Jingzhe, Lei & Way, Kuo, 2022. "Bayesian support vector machine for optimal reliability design of modular systems," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    14. Wang, Zhuoyang & Chen, Guo & Hill, David J. & Dong, Zhao Yang, 2016. "A power flow based model for the analysis of vulnerability in power networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 105-115.
    15. Zaretalab, Arash & Sharifi, Mani & Guilani, Pedram Pourkarim & Taghipour, Sharareh & Niaki, Seyed Taghi Akhavan, 2022. "A multi-objective model for optimizing the redundancy allocation, component supplier selection, and reliable activities for multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    16. Li, Chun-yang & Chen, Xun & Yi, Xiao-shan & Tao, Jun-yong, 2010. "Heterogeneous redundancy optimization for multi-state series–parallel systems subject to common cause failures," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 202-207.
    17. 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).
    18. Tian, Tianzi & Yang, Jun & Li, Lei & Wang, Ning, 2023. "Reliability assessment of performance-based balanced systems with rebalancing mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    19. 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.
    20. 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.

    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:ejores:v:221:y:2012:i:1:p:138-147. 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: http://www.elsevier.com/locate/eor .

    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.