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Greatest Lower Bounds of System Failure Probability in a Time Interval Under Incomplete Information About the Distribution Function of the Time to Failure

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Cybernetics and Systems Analysis Aims and scope

Abstract

The greatest lower bounds are obtained for the probability F(υ) − F(u), 0 < u < υ < ∞, in the class of distribution functions F(x) of nonnegative random variables with unimodal density with mode m<u and two first fixed moments.

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References

  1. L. S. Stoikova, “Exact upper bounds of the probability of failure in a time interval in the case of incomplete information on the distribution function,” Cybern. Syst. Analysis, 40, No. 5, 689–698 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  2. M. G. Krein and A. A. Nudelman, The Markov Moment Problem and Extremal Problems, Translations of Mathematical Monographs, Vol. 50, Amer. Math. Society (1977).

  3. G. M. Fikhtengolts, The Fundamentals of Mathematical Analysis, Vol. 2, Pure and Applied Mathematics Monograph, Pergamon Press (1965).

  4. L. S. Stoikova, “Necessary and sufficient conditions of existence of extreme distributionsF 5 -F 7 in the generalized Chebyshev inequalities problem, Part II,” Cybern. Syst. Analysis, 39, No. 2, 284–290 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  5. L. S. Stoikova, “Generalized Chebyshev inequalities and their application in the mathematical theory of reliability,” Cybern. Syst. Analysis, 46, No. 3, 472–476 (2010).

    Article  MATH  MathSciNet  Google Scholar 

  6. I. N. Kovalenko and L. S. Stoikova, “About some extremum problems of reliability theory,” Izv. AN SSSR. Tekhn. Kibern., No. 6, 19–23 (1986).

  7. L. S. Stoikova and G. N. Sakovich, “Exact upper-bound estimates for distribution functions in the class of one-node distributions with fixed moments,” Dop. AN URSR, Ser. A, No 1, 28–31 (1988).

  8. A. N. Golodnikov, Yu. M. Ermoliev, and P. S. Knopov, “Estimating reliability parameters under insufficient information,” Cybern. Syst. Analysis, 46, No. 3, 443–459 (2010).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Kyiv, Ukraine

    L. S. Stoikova

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  1. L. S. Stoikova
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Correspondence to L. S. Stoikova.

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Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2015, pp. 108–116.

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Stoikova, L.S. Greatest Lower Bounds of System Failure Probability in a Time Interval Under Incomplete Information About the Distribution Function of the Time to Failure. Cybern Syst Anal 51, 253–260 (2015). https://doi.org/10.1007/s10559-015-9717-x

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  • DOI: https://doi.org/10.1007/s10559-015-9717-x

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