Skip to main content
SpringerLink
Log in

System Reliability Analysis Method Based on Fuzzy Probability

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

Conventional methods for analyzing system reliability involve the use of unit reliability and system composition. However, these methods have limitation on considering the type of failure distribution that exists in unit of system, resulting in inaccurate evaluation of system reliability as the bathtub curve. The process in which unit and system go from a normal working state to a failure state can be described as a fuzzy process. The fuzzy probability of unit reliability is defined in formula, and its curve is drawn based on bathtub curve, reliability function curve and fuzzy probability. For two systems that have the same system reliability, conventional methods also fail to take into account the effect of differences in unit reliability on system reliability. In this study, we introduce a novel method to analyze system reliability that based on fuzzy probability. This method is an assumption that unit reliability is a fuzzy probability-based event, and then these concepts of system failure probability and integrated system reliability are proposed. The system failure probability is a characteristic quantity used to measure the effect of different unit in system reliability. The integrated system reliability is a characteristic quantity that evaluated the comprehensive system reliability. These proposed concepts are applied in the reliability analysis of series system, parallel system and compound system. These results verify the effectiveness of the proposed method by the application and comparison in these examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Yan, M.Q., Yang, B., Wang, Z.: Reliability assessment for multistate system subject to imperfect fault coverage. J. Xi’An Jiao Tong Univ. 45(10), 109–114 (2011)

    MATH  Google Scholar 

  2. Fang, Y.R., Kan, S.L., Yang, M., Xie, C., Pei, X.S.: Application of fuzzy multi-state Bayesian networks in redundant hydraulic system’s reliability analysis. Comput. Integr. Manuf. Syst. 21(7), 1856–1864 (2015)

    Google Scholar 

  3. Xing, L.D., Dai, Y.S.: A new decision diagram based method for efficient analysis on multi-state systems. IEEE Trans. Dependable Secure Comput. 6(3), 161–174 (2009)

    Article  MathSciNet  Google Scholar 

  4. Li, W.J., Pham, H.: Reliability modeling of multi-state degraded systems with multi-competing failures and random shocks. IEEE Trans. Reliab. 54(2), 297–303 (2005)

    Article  Google Scholar 

  5. Yeh, W.C.: The k-out-of-n acyclic multistate-node networks reliability evaluation using the universal generating function method. Reliab. Eng. Syst. Saf. 91(7), 800–808 (2006)

    Article  Google Scholar 

  6. Levitin, G., Xing, L.D.: Reliability and performance of multi-state systems with propagated failures having selective effect. Reliab. Eng. Syst. Saf. 95(6), 655–661 (2010)

    Article  Google Scholar 

  7. Levitin, G., Lisnianski, A., Ben-Haim, H., Elmakis, D.: Redundancy optimization for series–parallel multi-state systems. IEEE Trans. Reliab. 47(2), 165–172 (1998)

    Article  Google Scholar 

  8. Ding, Y., Zuo, M.J., Lisnianski, A., Tian, Z.G.: Fuzzy multi-state system: general definitions and performance assessment. IEEE Trans. Reliab. 57(4), 589–594 (2008)

    Article  Google Scholar 

  9. Li, Y.F., Ding, Y., Zio, E.: Random fuzzy extension of the universal generating function approach for the reliability assessment of multi-state systems under aleatory and epistemic uncertainties. IEEE Trans. Reliab. 63(1), 13–25 (2014)

    Article  Google Scholar 

  10. Huang, J., Zuo, M.J.: Dominant multi-state systems. IEEE Trans. Reliab. 53(3), 362–368 (2004)

    Article  Google Scholar 

  11. Xing, L., Dugan, J.B.: A separable ternary decision diagrams based analysis of generalized phased-mission reliability. IEEE Trans. Reliab. 53(2), 174–184 (2004)

    Article  Google Scholar 

  12. Xing L.: Efficient analysis of systems with multiple states. In: Proceedings of the IEEE 21st International Conference on Advanced Information Networking and Applications, May 2007, pp. 666–672

  13. Shrestha, A., Xing, I.D.: A logarithmic binary decision diagram-based method Ion multistate system analysis. IEEE Trans. Reliab. 57(4), 595–606 (2008)

    Article  Google Scholar 

  14. Vaurio, J.K.: The theory and quantification of common-cause shock events for redundant standby systems. Reliab. Eng. Syst. Saf. 43(3), 289–305 (1994)

    Article  Google Scholar 

  15. Chae, K.C., Clark, G.M.: System reliability in the presence of common-cause failures. IEEE Trans. Reliab. 35(1), 32–35 (1986)

    Article  MATH  Google Scholar 

  16. Vaurio, J.K.: An implicit method for incorporating common-cause failures in system analysis. IEEE Trans. Reliab. 47(2), 173–180 (1998)

    Article  Google Scholar 

  17. Levitin, G.: Incorporating common-cause failures into non repairable multistate series-parallel system analysis. IEEE Trans. Reliab. 5(4), 380–388 (2001)

    Article  Google Scholar 

  18. Yeh, W.C., Lin, Y.C., Chung, Y.Y., Chih, M.: A particle swarm optimization approach based on Monte Carlo simulation for solving the complex network reliability problem. IEEE Trans. Reliab. 59(1), 212–221 (2010)

    Article  Google Scholar 

  19. González-Fernández, R.A., Leite da Silva, A.M.: Reliability assessment of time-dependent systems via sequential cross-entropy Monte Carlo simulation. IEEE Trans. Power Syst. 26(4), 2381–2389 (2011)

    Article  Google Scholar 

  20. Wang, H., Thorp, J.S.: Optimal locations for protection system enhancement: a simulation of cascading outages. IEEE Trans. Power Deliv. 16(4), 528–533 (2001)

    Article  Google Scholar 

  21. Johnson, V.E.: A hierarchical model for estimating the early reliability of complex systems. IEEE Trans. Reliab. 54(2), 224–231 (2005)

    Article  Google Scholar 

  22. Brian, H., Ali, M.: A reliability growth projection model for one-shot systems. IEEE Trans. Reliab. 57(1), 174–181 (2008)

    Article  Google Scholar 

  23. Ali, A.R.K.: Circuit breaker condition assessment through a fuzzy-probabilistic analysis of actuating coil’s current. IET Gener. Transm. Distrib. 10(1), 48–56 (2016)

    Article  Google Scholar 

  24. Sallak, M., Simon, C., Aubry, J.F.: A fuzzy probabilistic approach for determining safety integrity level. IEEE Trans. Fuzzy Syst. 16(1), 239–248 (2008)

    Article  Google Scholar 

  25. Li, W.Y., Zhou, J.Q., Lu, J.P., Yan, W.: Incorporating a combined fuzzy and probabilistic load model in power system reliability assessment. IEEE Trans. Power Syst. 21(3), 1368–1388 (2007)

    Google Scholar 

  26. Dunyak, J., Saad, I.W., Wunsch, D.: A theory of independent fuzzy probability for system reliability. IEEE Trans. Fuzzy Syst. 7(2), 286–294 (1999)

    Article  Google Scholar 

  27. Wang, J.D., Liu, T.S.: Fuzzy reliability using a discrete stress-strength interference model. IEEE Trans. Reliab. 45(1), 145–149 (1996)

    Article  Google Scholar 

  28. Kenarangui, Rasool: Event-tree analysis by fuzzy probability. IEEE Trans. Reliab. 40(1), 120–124 (1991)

    Article  MATH  Google Scholar 

  29. Ma, D.Z., Zhou, Z., Yu, X.Y., Fan, S.C., Xing, W.W., Guo, Z.S.: Reliability analysis of multi-state Bayesian networks based on fuzzy probability. Syst. Eng. Electron. 34(12), 2607–2611 (2012)

    Google Scholar 

  30. Tanaka, H., Fan, L.T., Lai, F.S., Toguch, K.I.: Fault-tree analysis by fuzzy probability. IEEE Trans. Reliab. 32(5), 453–457 (1983)

    Article  MATH  Google Scholar 

  31. Mentes, A., Heluacioglu, I.H.: An application of fuzzy fault tree analysis for spread mooring systems. Ocean Eng. 38(2), 285–294 (2011)

    Article  Google Scholar 

  32. Song, H., Zhang, H.Y., Chan, C.W.: Fuzzy fault tree analysis based on T-S model with application to INS/GPS navigation system. Soft Comput. 13(1), 31–40 (2009)

    Article  Google Scholar 

  33. Qi, J., Hu, X., Gao, X.: Quantitative risk analysis of subsea pipeline and riser: an experts assessment approach using fuzzy fault tree. Int. J. Reliab. Saf. 8(1), 33–50 (2014)

    Article  Google Scholar 

  34. Sun, L.N., Huang, N., Wu, W.Q., Li, X.K.: Performance reliability of polymorphic systems by fuzzy fault tree based on T-S model. J. Mech. Eng. 52(10), 191–198 (2016)

    Article  Google Scholar 

  35. Liu, P., Cheng, X.Q., Qin, Y., Zhang, Y., Zhang, Z.Y.: Sliding plug door system reliability analysis based on fuzzy fault tree. J. Central South Univ. (Sci. Technol.) 44(s1), 310–314 (2013)

    Google Scholar 

  36. Yao, Y.C., Chen, D.N., Wang, B.: Fuzzy reliability assessment method based on T-S fault tree and Bayesian network. J. Mech. Eng. 50(2), 193–201 (2014)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 51377044), National Sci-Tech Support Plan (No. 2015BAA09B01), Hebei Province Higher School Science and Technology Research Youth Fund (No. QN2015102), and Science and Technology Support Program of Hebei Province (No. 15212117).

Author information

Authors and Affiliations

  1. School of Electrical Engineering, Hebei University of Technology, 8 Guangrong Rd., Hongqiao District, Tianjin City, 300310, China

    Zhi-Gang Li, Jun-Gang Zhou & Bo-Ying Liu

  2. Shandong Institute for Product Quality Inspection, 31000 Jingshidong Rd., Licheng District, Jinan City, 250102, China

    Jun-Gang Zhou

Authors
  1. Zhi-Gang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun-Gang Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bo-Ying Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhi-Gang Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, ZG., Zhou, JG. & Liu, BY. System Reliability Analysis Method Based on Fuzzy Probability. Int. J. Fuzzy Syst. 19, 1759–1767 (2017). https://doi.org/10.1007/s40815-017-0363-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-017-0363-5

Keywords

Search

Navigation