Automation and Remote Control

, Volume 78, Issue 1, pp 113–124 | Cite as

Reliability of repairable reserved systems with failure aftereffect

  • S. V. Gurov
  • L. V. UtkinEmail author
Safety, Viability, Reliability, Technical Diagnostics


We propose new models for analyzing the reliability of repairable systems with failure aftereffect, when the probability distribution of an element’s time to failure changes only during the time when another element is being repaired. The key idea here is the so-called coupling principle for various probability distributions when the system’s operation conditions or the “residual lifetime preservation condition” change. We show a method for constructing a system of integral equations as a universal tool for modeling the reliability of systems under the assumption that time to failure of each element obeys the Weibull distribution.

Key words

reliability aftereffect repairable system integral equations failure load time to failure Weibull distribution 


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  1. 1.
    Bebbington, M., Lai, C.-D., and Zitikis, R., Reliability of Modules with Load-Sharing Components, J. Appl. Math. Decision Sci., 2007, vol. 1, pp. 1–18.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Daniels, H., The Statistical Theory of the Strength of Bundles of Threads, Proc. Royal Soc. London Ser. A, 1945, vol. 183, pp. 405–435.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Dewan, I., Naik-Nimbalkar, U.V., Cochran, J.J., et al., Load-Sharing Systems, in Wiley Encyclopedia of Operations Research and Management Science, New York: Wiley, 2010.Google Scholar
  4. 4.
    Durham, S., Lee, S., and Lynch, J., On the Calculation of the Reliability of General Load Sharing Systems, J. Appl. Probab., 1995, vol. 32, pp. 777–792.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Gurov, S.V. and Utkin, L.V., Load-Share Reliability Models with the Piecewise Constant Load, Int. J. Reliabilit. Safet., 2012, vol. 6, no. 4, pp. 338–353.CrossRefGoogle Scholar
  6. 6.
    Gurov, S.V. and Utkin, L.V., A Continuous Extension of a Load-Share Reliability Model Based on a Condition of the Residual Lifetime Conservation, Eur. J. Indust. Eng., 2014, vol. 8, pp. 349–365.CrossRefGoogle Scholar
  7. 7.
    Huang, L. and Xu, Q., Lifetime Reliability for Load-Sharing Redundant Systems with Arbitrary Failure Distributions, IEEE Transact. Reliabil., 2010, vol. 59, no. 2, pp. 319–330.CrossRefGoogle Scholar
  8. 8.
    Jain, M. and Gupta, R., Load Sharing M–out of–N: G System with Non-Identical Components Subject to Common Cause Failure, Int. J. Math. Oper. Res., 2012, vol. 4, no. 5, pp. 586–605.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Kvam, P. and Pena, E., Estimating Load-Sharing Properties in a Dynamic Reliability System, J. Am. Statist. Associat., 2005, vol. 100, pp. 262–272.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Liu, H., Reliability of a Load-Sharing k-out-of-n: G System: Non-iid Components with Arbitrary Distributions, IEEE Transact. Reliabil., 1998, vol. 47, no. 3, pp. 279–284.CrossRefGoogle Scholar
  11. 11.
    Park, C., Parameter Estimation for the Reliability of Load-Sharing Systems, IIE Transact., 2010, vol. 42, no. 10, pp. 753–765.CrossRefGoogle Scholar
  12. 12.
    Park, C., Parameter Estimation from Load-Sharing System Data Using the Expectation–Maximization Algorithm, IIE Transact., 2013, vol. 45, no. 2, pp. 147–163.CrossRefGoogle Scholar
  13. 13.
    Qi, X., Zhang, Z., Zuo, D., and Yang, X., Optimal Maintenance Policy for High Reliability Load-Sharing Computer Systems with k-out-of-n:G Redundant Structure, Appl. Math. Inform. Sci., 2014, vol. 8, no. 1, pp. 341–347.CrossRefGoogle Scholar
  14. 14.
    Ross, S., A Model in which Component Failure Rates Depend on the Working Set, Naval Res. Logist. Quart., 1984, vol. 31, pp. 297–300.CrossRefzbMATHGoogle Scholar
  15. 15.
    Singh, B. and Gupta, P.K., Load-Sharing System Model and Its Application to the Real Data Set, Math. Comput. Simulat., 2012, vol. 82, no. 9, pp. 1615–1629.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Volovoi, V., Universal Failure Model for Multi-Unit Systems with Shared Functionality, Reliabil. Eng. Syst. Safety, 2013, vol. 119, pp. 141–149.CrossRefGoogle Scholar
  17. 17.
    Yang, K. and Younis, H., A Semi-Analytical Monte Carlo Simulation Method for System’s Reliability with Load Sharing and Damage Accumulation, Reliabil. Engineer. Syst. Safety, 2005, vol. 87, pp. 191–200.CrossRefGoogle Scholar
  18. 18.
    Yinghui, T. and Jing, Z., New Model for Load-Sharing k-out-of-n: G System with Different Components, J. Syst. Engineer. Electron., 2008, vol. 19, no. 4, pp. 748–751.CrossRefzbMATHGoogle Scholar
  19. 19.
    Yun, W.Y., Kim, G.R., and Yamamoto, H., Economic Design of a Load-Sharing Consecutive k-out-of-n: F System, IIE Transact., 2012, vol. 44, no. 1, pp. 55–67.CrossRefGoogle Scholar
  20. 20.
    Polovko, A.M. and Gurov, S.V., Osnovy teorii nadezhnosti (Fundamentals of Reliability Theory), St. Petersburg: BKhV-Peterburg, 2006.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.St. Petersburg State Forest Engineering UniversitySt. PetersburgRussia
  2. 2.Peter the Great St. Petersburg Polytechnical UniversitySt. PetersburgRussia

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