Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 2567–2577 | Cite as

Reliability Modeling of Redundant Systems Considering CCF Based on DBN

  • Zhiqiang LiEmail author
  • Tingxue Xu
  • Junyuan Gu
  • Haowei Wang
  • Jianzhong Zhao
Research Article - Systems Engineering


Common cause failure (CCF) has become a hot topic in reliability and availability analysis of redundant systems. Aiming at the shortage of \(\beta \)-factor model in distinguishing three or more failures, multiple error shock theory is put forward. Having the problem in determining minimal cut sets and structure functions for dynamic fault tree (DFT), dynamic Bayesian network (DBN) is applied to transit DFT events to corresponding nodes and express causal relations between the nodes. On the base of explicit modeling for CCF, DBN models for hot spare (HSP) gate, cold spare (CSP) gate and warm spare (WSP) gate are established considering CCF processes. For a HSP gate, all failure processes are listed in the stress event layer for each component. For a CSP gate and a WSP gate, CCF node and intermediate nodes are introduced to express causal relations. At last, a control unit and its improved type are taken as examples. The DBN models are built by referring to corresponding DFT structures when taking CCFs into consideration. From the results, it is obvious that the modern unit has a relative higher reliability and availability. And it is less easily influenced by uncertainty such as failure rates and coverage factor through sensitivity analysis.


Common cause failure Multiple error shock Dynamic spare gate Dynamic Bayesian network Dynamic fault tree 


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  1. 1.
    Bentolhoda, J.; Lance, F.: A universal generating function-based multi-state system performance model subject to correlated failures. Reliab. Eng. Syst. Saf. 152, 16–27 (2016)CrossRefGoogle Scholar
  2. 2.
    Hauge, S.; Hokstad, P.; Habrekke, S.; Lundteigen, M.A.: Common cause failures in safety-instrumented systems: using field experience from the petroleum industry. Reliab. Eng. Syst. Saf. 151, 34–35 (2016)CrossRefGoogle Scholar
  3. 3.
    Albert, K.; Gunnar, J.: Recent insights from the international common-cause failure data exchange project. Nucl. Eng. Technol. 49, 327–334 (2017)CrossRefGoogle Scholar
  4. 4.
    Vaurio, J.K.: Consistent mapping of common cause failure rates and alpha factors. Reliab. Eng. Syst. Saf. 92, 628–645 (2007)CrossRefGoogle Scholar
  5. 5.
    Vaurio, J.K.: Extensions of the uncertainty quantification of common cause failure rates. Reliab. Eng. Syst. Saf. 78, 63–69 (2002)CrossRefGoogle Scholar
  6. 6.
    Yu, H.; Yang, J.; Lin, J.; Zhao, Y.: Reliability evaluation of non-repairable phased-mission common bus systems with common cause failures. Comput. Ind. Eng. 111, 445–457 (2017)CrossRefGoogle Scholar
  7. 7.
    Muhammad, Z.; Qazi, M.; Nouman, A.: Calculation and updating of common cause failure unavailability by using alpha factor model. Ann. Nucl. Energy 90, 106–114 (2016)CrossRefGoogle Scholar
  8. 8.
    David, M.; Martin, N.; Norman, F.: Solving dynamic fault trees using a new hybrid Bayesian network inference algorithm. In: The 16th Mediterranean Conference on Control and Automation, Congress Centre, Ajaccio, France, 25–27 June (2008)Google Scholar
  9. 9.
    Fan, D.M.; Wang, Z.L.; Liu, L.L.; Ren, Y.: A modified GO-FLOW methodology with common cause failure based on Discrete Time Bayesian Network. Nucl. Eng. Des. 305, 476–488 (2016)CrossRefGoogle Scholar
  10. 10.
    Xing, L.; Boddu, P.; Sun, Y.; Wang, W.: Reliability analysis of static and dynamic fault-tolerant systems subject to probabilistic common-cause failures. Proc. ImechE Part O J. Risk Reliab. 224, 43–53 (2009)Google Scholar
  11. 11.
    Li, Y.F.; Mi, J.H.; Huang, H.Z.; Zhu, S.P.; Xiao, N.C.: Fault tree analysis of train rear-end collision accident considering common cause failure. Eksploat Niezawodn 15, 403–408 (2013)Google Scholar
  12. 12.
    Ziva, B.R.; Marko, C.: An extension of Multiple Greek Letter method for common cause failures modelling. J. Loss Prevent. Proc. 29, 144–154 (2014)CrossRefGoogle Scholar
  13. 13.
    Zheng, X.Y.; Akira, Y.; Takashi, T.: \(\upalpha \)-Decomposition for estimating parameters in common cause failure modeling based on causal inference. Reliab. Eng. Syst. Saf. 116, 20–27 (2013)CrossRefGoogle Scholar
  14. 14.
    Corwin, L.A.; Dana, L.K.: The binomial failure rate common-cause model with WinBUGS. Reliab. Eng. Syst. Saf. 94, 990–999 (2009)CrossRefGoogle Scholar
  15. 15.
    Cai, B.P.; Liu, Y.H.; Liu, Z.K.; Tian, X.J.; Zhang, Y.Z.; Liu, J.: Performance evaluation of subsea blowout preventer systems with common-cause failures. J. Petrol. Sci. Eng. 90, 18–25 (2012)CrossRefGoogle Scholar
  16. 16.
    Liu, Z.K.; Liu, Y.H.; Cai, B.P.; Zhang, D.W.; Zheng, C.: Dynamic Bayesian network modeling of reliability of subsea blowout preventer stack in presence of common cause failures. J. Loss Prevent. Proc. 38, 58–66 (2015)CrossRefGoogle Scholar
  17. 17.
    Wang, L.Q.; Zhou, W.J.; Wei, X.S.; Zhai, L.L.; Wu, G.K.: A coupling vibration model of multi-stage pump rotor system based on FEM. Mechanika 22, 31–37 (2016)Google Scholar
  18. 18.
    Kang, F.; Liu, J.; Li, J.J.; Li, S.J.: Concrete dam deformation prediction model for health monitoring based on extreme learning machine. Struct. Control Health 24, e1997 (2017)CrossRefGoogle Scholar
  19. 19.
    Kang, F.; Xu, Q.; Li, J.J.: Slope reliability analysis using surrogate models via new support vector machines with swarm intelligence. Appl. Math. Model. 40, 6105–6120 (2016)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Marko, C.; Borut, M.: A dynamic fault tree. Reliab. Eng. Syst. Saf. 75, 83–91 (2002)CrossRefGoogle Scholar
  21. 21.
    Yevkin, O.: An efficient approximate Markov chain method in dynamic fault tree analysis. Qual. Reliab. Eng. Int. 32, 1509–1520 (2016)CrossRefGoogle Scholar
  22. 22.
    Li, Y.F.; Huang, H.Z.; Liu, Y.; Xiao, N.C.; Li, H.Q.: A new fault tree analysis method: fuzzy dynamic fault tree analysis. Eksploat Niezawodn 14, 208–214 (2012)Google Scholar
  23. 23.
    Zhu, P.C.; Han, J.; Liu, L.B.; Fabrizio, L.: A stochastic approach for the analysis of dynamic fault trees with spare gates under probabilistic common cause failures. IEEE Trans. Reliab. 64, 878–892 (2015)CrossRefGoogle Scholar
  24. 24.
    Shubharthi, B.; Gao, X.D.; Hans, P.; Mannan, M.S.: Bayesian network based dynamic operational risk assessment. J. Loss Prevent. Proc. 41, 399–410 (2016)CrossRefGoogle Scholar
  25. 25.
    Esmaeil, Z.; Ali, A.; Nima, K.; Mostafa, M.A.; Iraj, M.: Dynamic safety assessment of natural gas stations using Bayesian network. J. Hazard. Mater. 321, 830–840 (2017)CrossRefGoogle Scholar
  26. 26.
    Li, Z.Q.; Xu, T.X.; Gu, J.Y.; An, J.; Dong, Q.: Availability modeling and analyzing of multi-state control unit under condition-based maintenance. Acta ArmamentarII 38, 2240–2250 (2017)Google Scholar
  27. 27.
    Andrew, O.C.; Ali, M.: A general cause based methodology for analysis of common cause and dependent failures in system risk and reliability assessments. Reliab. Eng. Syst. Saf. 145, 341–350 (2016)CrossRefGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  • Zhiqiang Li
    • 1
    Email author
  • Tingxue Xu
    • 1
  • Junyuan Gu
    • 1
  • Haowei Wang
    • 1
  • Jianzhong Zhao
    • 1
  1. 1.Naval Aeronautical UniversityYantaiChina

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