IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v133y2015icp1-10.html
   My bibliography  Save this article

Discrete and continuous reliability models for systems with identically distributed correlated components

Author

Listed:
  • Fiondella, Lance
  • Xing, Liudong

Abstract

Many engineers and researchers base their reliability models on the assumption that components of a system fail in a statistically independent manner. This assumption is often violated in practice because environmental and system specific factors contribute to correlated failures, which can lower the reliability of a fault tolerant system. A simple method to quantify the impact of correlation on system reliability is needed to encourage models explicitly incorporating correlated failures. Previous approaches to model correlation are limited to systems consisting of two or three components or assume that the majority of the subsets of component failures are statistically independent. This paper proposes a method to model the reliability of systems with correlated identical components, where components possess the same reliability and also exhibit a common failure correlation parameter. Both discrete and continuous models are proposed. The method is demonstrated through a series of examples, including derivations of analytical expressions for several common structures such as k-out-of-n: good and parallel systems. The continuous models consider the role of correlation on reliability and metrics, including mean time to failure, availability, and mean residual life. These examples illustrate that the method captures the impact of component correlation on system reliability and related metrics.

Suggested Citation

  • Fiondella, Lance & Xing, Liudong, 2015. "Discrete and continuous reliability models for systems with identically distributed correlated components," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 1-10.
    • Handle: RePEc:eee:reensy:v:133:y:2015:i:c:p:1-10
    DOI: 10.1016/j.ress.2014.08.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832014001975
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2014.08.004?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. Lance Fiondella & Swapna S. Gokhale, 2010. "Estimating system reliability with correlated component failures," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 4(2/3), pages 188-205.
    2. Xing, Liudong & Meshkat, Leila & Donohue, Susan K., 2007. "Reliability analysis of hierarchical computer-based systems subject to common-cause failures," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 351-359.
    3. Xing, Liudong & Levitin, Gregory, 2013. "BDD-based reliability evaluation of phased-mission systems with internal/external common-cause failures," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 145-153.
    4. Levitin, Gregory & Xing, Liudong, 2010. "Reliability and performance of multi-state systems with propagated failures having selective effect," Reliability Engineering and System Safety, Elsevier, vol. 95(6), pages 655-661.
    5. Modarres, Reza, 2011. "High-dimensional generation of Bernoulli random vectors," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1136-1142, August.
    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. Jafary, Bentolhoda & Fiondella, Lance, 2016. "A universal generating function-based multi-state system performance model subject to correlated failures," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 16-27.
    2. Hüseyin Sarper, 2019. "Correlated reliability and an application: Propulsive landing on Mars," Journal of Risk and Reliability, , vol. 233(5), pages 826-846, October.
    3. Park, Jae-Hyun, 2017. "Time-dependent reliability of wireless networks with dependent failures," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 47-61.
    4. Tavangar, Mahdi & Bairamov, Ismihan, 2015. "On conditional residual lifetime and conditional inactivity time of k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 225-233.
    5. Liu, Xiang-dong & Pan, Fei & Cai, Wen-li & Peng, Rui, 2020. "Correlation and risk measurement modeling: A Markov-switching mixed Clayton copula approach," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    6. Xiang-Yu Li & Yu Liu & Chu-Jie Chen & Tao Jiang, 2016. "A copula-based reliability modeling for nonrepairable multi-state k-out-of-n systems with dependent components," Journal of Risk and Reliability, , vol. 230(2), pages 133-146, April.
    7. Rychlik, Tomasz, 2017. "Evaluations of quantiles of system lifetime distributions," European Journal of Operational Research, Elsevier, vol. 256(3), pages 935-944.
    8. Konul Bayramoglu Kavlak, 2017. "Reliability and mean residual life functions of coherent systems in an active redundancy," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(1), pages 19-28, February.
    9. Yi-Kuei Lin & Lance Fiondella & Ping-Chen Chang, 2022. "Reliability of time-constrained multi-state network susceptible to correlated component faults," Annals of Operations Research, Springer, vol. 311(1), pages 239-254, April.
    10. Beck, André T. & Rodrigues da Silva, Lucas A. & Miguel, Leandro F.F., 2023. "The latent failure probability: A conceptual basis for robust, reliability-based and risk-based design optimization," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    11. Elmira Yu. Kalimulina, 2017. "Analysis of system reliability with control, dependent failures, and arbitrary repair times," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(1), pages 180-188, March.

    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. Fan, Mengfei & Zeng, Zhiguo & Zio, Enrico & Kang, Rui & Chen, Ying, 2018. "A stochastic hybrid systems model of common-cause failures of degrading components," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 159-170.
    2. Zhang, Chao & Xu, Xin & Dui, Hongyan, 2020. "Analysis of network cascading failure based on the cluster aggregation in cyber-physical systems," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    3. Cheng, Chen & Yang, Jun & Li, Lei, 2021. "Reliability evaluation of a k-out-of-n(G)-subsystem based multi-state phased mission system with common bus performance sharing subjected to common cause failures," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    4. Peng Su & Guanjun Wang, 2022. "Reliability analysis of network systems subject to probabilistic propagation failures and failure isolation effects," Journal of Risk and Reliability, , vol. 236(2), pages 290-306, April.
    5. Jafary, Bentolhoda & Fiondella, Lance, 2016. "A universal generating function-based multi-state system performance model subject to correlated failures," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 16-27.
    6. Wang, Chaonan & Xing, Liudong & Levitin, Gregory, 2013. "Reliability analysis of multi-trigger binary systems subject to competing failures," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 9-17.
    7. Peng, Rui & Wu, Di & Xiao, Hui & Xing, Liudong & Gao, Kaiye, 2019. "Redundancy versus protection for a non-reparable phased-mission system subject to external impacts," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    8. Park, Jae-Hyun, 2017. "Time-dependent reliability of wireless networks with dependent failures," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 47-61.
    9. Matsuoka, Takeshi, 2023. "Reliability analysis of a BWR plant system at startup stage  - analysis by the GO-FLOW methodology with consideration of loop structures and phased mission problem -," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    10. Tang, Maochun & Xiahou, Tangfan & Liu, Yu, 2023. "Mission performance analysis of phased-mission systems with cross-phase competing failures," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    11. Fang, Jiayue & Kang, Rui & Chen, Ying, 2021. "Reliability evaluation of non-repairable systems with failure mechanism trigger effect," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    12. Zaitseva, Elena & Levashenko, Vitaly & Kostolny, Jozef, 2015. "Importance analysis based on logical differential calculus and Binary Decision Diagram," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 135-144.
    13. Yuchang Mo & Liudong Xing, 2013. "An enhanced decision diagram-based method for common-cause failure analysis," Journal of Risk and Reliability, , vol. 227(5), pages 557-566, October.
    14. Li, Shumin & Si, Shubin & Dui, Hongyan & Cai, Zhiqiang & Sun, Shudong, 2014. "A novel decision diagrams extension method," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 107-115.
    15. Levitin, Gregory & Xing, Liudong & Huang, Hong Zhong, 2019. "Dynamic availability and performance deficiency of common bus systems with imperfectly repairable components," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 58-66.
    16. Wang, Chaonan & Xing, Liudong & Peng, Rui & Pan, Zhusheng, 2017. "Competing failure analysis in phased-mission systems with multiple functional dependence groups," Reliability Engineering and System Safety, Elsevier, vol. 164(C), pages 24-33.
    17. Levitin, Gregory & Xing, Liudong & Ben-Haim, Hanoch & Dai, Yuanshun, 2011. "Multi-state systems with selective propagated failures and imperfect individual and group protections," Reliability Engineering and System Safety, Elsevier, vol. 96(12), pages 1657-1666.
    18. Modarres, Reza, 2014. "On the interpoint distances of Bernoulli vectors," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 215-222.
    19. Dui, Hongyan & Meng, Xueyu & Xiao, Hui & Guo, Jianjun, 2020. "Analysis of the cascading failure for scale-free networks based on a multi-strategy evolutionary game," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    20. Jung, Woo Sik, 2015. "A method to improve cutset probability calculation in probabilistic safety assessment of nuclear power plants," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 134-142.

    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:133:y:2015:i:c:p:1-10. 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.