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Operator semi-group of density evolution equation for a repairable redundant system with two same components

  • Applied Mathematics And Mechanics
  • Published:
Journal of Shanghai University (English Edition)

Abstract

For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations, called density evolution equations. It was proved that the time-dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi-group method. In this proof, it is not necessary to suppose that the repair rate function is bounded. The technique of the proof is valuable for many density evolution equations.

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References

  1. Fattorini H O. The Cauchy Problems[M]. Addison-Wesley. Massachusetts, 1983.

    Google Scholar 

  2. Gupur G, Li X Z, Zhu G T. Functional Analysis Method in Queueng Theory [M]. Research Information Ltd., UK, 2001.

    Google Scholar 

  3. Shi D H. Density Evolution Method in Stochastic Models [M]. Science Press, Beijing, 1999(in Chinese).

    Google Scholar 

  4. Lang S. Real Analysis [M]. Addison-Wesley Publishing Com., London, 1983.

    Google Scholar 

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Additional information

Project supported by the National Natural Science Foundation of China(Grant No. 70171059)

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Shi, DH., Xu, H., Xiong, Y. et al. Operator semi-group of density evolution equation for a repairable redundant system with two same components. J. of Shanghai Univ. 6, 278–281 (2002). https://doi.org/10.1007/s11741-002-0050-z

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  • DOI: https://doi.org/10.1007/s11741-002-0050-z

Key words

MSC 2000

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