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

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  • 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
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    References listed on IDEAS

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    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.
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    Citations

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    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. Rychlik, Tomasz, 2017. "Evaluations of quantiles of system lifetime distributions," European Journal of Operational Research, Elsevier, vol. 256(3), pages 935-944.
    3. 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.
    4. Hüseyin Sarper, 2019. "Correlated reliability and an application: Propulsive landing on Mars," Journal of Risk and Reliability, , vol. 233(5), pages 826-846, October.
    5. 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.
    6. 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.
    7. 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.
    8. 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).
    9. Yu Zang & Jiaxiang E & Lance Fiondella, 2024. "A Network Reliability Analysis Method for Complex Real-Time Systems: Case Studies in Railway and Maritime Systems," Mathematics, MDPI, vol. 12(19), pages 1-30, September.
    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. 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.
    12. 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.

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