The Properties of Order and Failure Estimation on Redundancy System

  • Lin Xu
  • Chao-Fan Xie
  • Lu-Xiong Xu
  • Fuquan Zhang
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 110)


Redundant backup system is a common system in the real world, especially in aviation, electromechanics and other fields. Therefore, it is meaningful to give the parameter estimation of redundant systems. Previous research has given some results about the order and failure rate of the redundancy distributed redundant backup system, thus providing consumers with a computed and measurable product reliability calculation method. By using the irreplaceable censored life test, Providing a statistical significance of the estimation formula. However, the properties of estimation are not given and how to improve it. The study gives the estimation properties in probabilistic sense, which is asymptotic convergence in probability. Continue to improve the estimator on variance, so as to achieve asymptotic minimum consistent variance estimation. This ensures that the given estimation formula is available in practice.


Redundant backup Estimation formula Exponential distribution 



This research was partially supported by Fujian Province Education Hall Youth Project (number: JAT170679), by the Electronic information and engineering institute of Fujian Normal University, by the Institute of Innovative Information Industry of Fujian Normal University, and the School of Economic of Fujian Normal University.


  1. 1.
    Luss, H.: An inspection policy model for production facilities. Manag. Sci. 29, 101–109 (1983)CrossRefGoogle Scholar
  2. 2.
    Leung, K.N.F., Lai, K.K.: A preventive maintenance and re-placement policy of a series system with failure interaction. Optimization 61(2), 223–237 (2012)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Sung, C.K., Sheu, S.H., Hsu, T.S., Chen, Y.C.: Extended optimal replacement policy for a two-unit system with failure rate interaction and external shocks. Int. J. Syst. Sci. 44(5), 877–888 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Lai, M.T., Yan, H.: Optimal number of minimal repairs with cumulative repair cost limit for a two-unit system with failure rate interactions. Int. J. Syst. Sci. 47(2), 466–473 (2014)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Merle, G.: Algebraic modeling of dynamic fault trees, contribution to qualitative and quantitative analysis. ENS de Caehan, France (2010)Google Scholar
  6. 6.
    Liang, X., Hong, Y., Zhang, Y., et al.: Numerical simulation to reliability analysis of fault-tolerant repairable system. J. Shanghai Jiaotong Univ. 15(5), 526–534 (2010)CrossRefGoogle Scholar
  7. 7.
    Ye, Z.S., Wang, Y., Tsui, K.L., et al.: Degradation data analysis using wiener processes with measurement errors. IEEE Trans. Reliab. 62(4), 772–780 (2013)CrossRefGoogle Scholar
  8. 8.
    Fan, J.J., Yung, K.C., Michael, P.: Lifetime estimation of high-power white LED using degradation data driven method. IEEE Trans. Device Mater. Reliab. 12(2), 470–477 (2012)CrossRefGoogle Scholar
  9. 9.
    Ye, Z.S., Wang, Y., Tsui, K.L., et al.: Degradation data analysis using wiener processes with measurement errors. IEEE Trans. Reliab. 62(4), 772–780 (2013)CrossRefGoogle Scholar
  10. 10.
    Laurenciu, N.C., Cotofana, S.D.: A nonlinear degradation path dependent end-of-life estimation framework from noisy observations. Microelectron. Reliab. 53, 1213–1217 (2013)CrossRefGoogle Scholar
  11. 11.
    Zhai, G.F., Zhou, Y.G., Ye, X.R., et al.: A method of multi-objective reliability tolerance design for electronic circuits. Chin. J. Aeronaut. 26(1), 161–170 (2013)CrossRefGoogle Scholar
  12. 12.
    Xu, L., Xie, C.F., Xu, L.X.: Reliability envelope analysis. J. Comput. 25(4), 26–34 (2014)MathSciNetGoogle Scholar
  13. 13.
    Xu, L., Xie, C.F., Xu, L.X.: Reliability Envelope Analysis. Advances in Intelligent System Computing, vol. 535, pp. 35-42 (2017)Google Scholar
  14. 14.
    Xie, C.F., Xu, L., Xu, L.X., Zhang, F.: The order and failure estimation of redundancy system based on cobweb model. In: The Fourth Euro-China Conference on Intelligent Data Analysis and Applications, pp. 64–72 (2018)Google Scholar
  15. 15.
    Cramer: Statistical mathematics method. Shanghai: Shanghai science and Technology Press (1982)Google Scholar
  16. 16.
    Rao, C.R.: Linear Statistical Inference and its Applications, 2nd edn. Wiley, New York (1975)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Lin Xu
    • 1
  • Chao-Fan Xie
    • 2
  • Lu-Xiong Xu
    • 2
  • Fuquan Zhang
    • 3
    • 4
  1. 1.Key Laboratory of Nondestructive TestingFuqing Branch of Fujian Normal UniversityFuqing, Fuzhou CityChina
  2. 2.Fuqing Branch of Fujian, Normal University, Electronic Information and Engineering InstituterFuqing, Fuzhou CityChina
  3. 3.Fujian Provincial Key Laboratory of Information Processing and Intelligent ControlMinjiang UniversityFuzhouChina
  4. 4.School of SoftwareBeijing Institute of TechnologyBeijingChina

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