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Stochastic Models of Systems in Reliability Problems

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Statistical and Probabilistic Models in Reliability

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

Problems of singular perturbation of a reducible invertible operator are applied to reliability analysis of stochastic systems. Heuristic principles of phase merging and diffusion approximation are described.

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References

  1. Gnedenko, B. V. (1964a). On spare duplication, Technical Cybernetics, 4, 3–12.

    MathSciNet  Google Scholar 

  2. Gnedenko, B. V. (1964b). On duplication with renewal, Technical Cybernetics, 5, 111–118.

    Google Scholar 

  3. Soloviev, A. D. (1964). Asymptotical distribution of the lifetime of a duplicated element, Technical Cybernetics, 5, 119–121.

    Google Scholar 

  4. Gnedenko, D. B. and Soloviev A. D. (1975). A general model for standby with renewal, Technical Cybernetics, 6.

    Google Scholar 

  5. Korolyuk, V. S. (1965). The sojourn time of semi-Markov process in a subset of states, Ukrainian Mathematics Journal.

    Google Scholar 

  6. Korolyuk, V. S. and Turbin, A. F. (1993). Mathematical Foundation of the State Lumping of Large Systems, Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Book  Google Scholar 

  7. Korolyuk, V. S. and Swishchuk, A. V. (1995). Evolution of Systems in Random Media, Boca Raton, FL: CRC Press.

    Google Scholar 

  8. Korolyuk, V. S. and Korolyuk, V. V. (1997). Stochastic Models of Systems, Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  9. Anisimov, V. V. and Lebedev, E. A. (1992). Stochastic queueing networks, Kyiv. Lybid. (in Ukrainian).

    Google Scholar 

  10. Feller, W. (1958). An Introduction to Probability Theory and its Applications, Vol. I, New York: John Wiley & Sons.

    Google Scholar 

  11. Derzko, N. A. and Korolyuk, V. V. (1997). Repairman problem with limited service, Preprint, University of Toronto, Canada.

    Google Scholar 

  12. Korolyuk, V. S., Derzko, N. A. and Korolyuk, V. V. (1998). Markovian repairman problems. Classification and Approximation.

    Google Scholar 

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© 1999 Springer Science+Business Media New York

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Korolyuk, V.S. (1999). Stochastic Models of Systems in Reliability Problems. In: Ionescu, D.C., Limnios, N. (eds) Statistical and Probabilistic Models in Reliability. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1782-4_9

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  • DOI: https://doi.org/10.1007/978-1-4612-1782-4_9

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7280-9

  • Online ISBN: 978-1-4612-1782-4

  • eBook Packages: Springer Book Archive

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