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Consecutive k-within-m-out-of-n:F system with exchangeable components

Author

Listed:
  • Eryilmaz, Serkan
  • Kan, Cihangir
  • Akici, Fatih

Abstract

As a generalization of k-out-of-n:F and consecutive k-out-of-n:F systems, the consecutive k-within-m-out-of-n:F system consists of n linearly ordered components such that the system fails iff there are m consecutive components which include among them at least k failed components. In this article, the reliability properties of consecutive k-within-m-out-of-n:F systems with exchangeable components are studied. The bounds and approximations for the survival function are provided. A Monte Carlo estimator of system signature is obtained and used to approximate survival function. The results are illustrated and numerics are provided for an exchangeable multivariate Pareto distribution.

Suggested Citation

  • Eryilmaz, Serkan & Kan, Cihangir & Akici, Fatih, 2009. "Consecutive k-within-m-out-of-n:F system with exchangeable components," MPRA Paper 26838, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:26838
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    File URL: https://mpra.ub.uni-muenchen.de/26838/1/MPRA_paper_26838.pdf
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    Citations

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    Cited by:

    1. repec:eee:reensy:v:95:y:2010:i:3:p:247-254 is not listed on IDEAS
    2. E. Salehi & M. Asadi & S. Eryılmaz, 2012. "On the mean residual lifetime of consecutive k-out-of-n systems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 93-115, March.
    3. Makri, Frosso S., 2011. "Minimum and maximum distances between failures in binary sequences," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 402-410, March.
    4. repec:eee:reensy:v:96:y:2011:i:5:p:564-568 is not listed on IDEAS
    5. Eryilmaz, Serkan, 2011. "The behavior of warm standby components with respect to a coherent system," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1319-1325, August.

    More about this item

    Keywords

    exchangeable lifetimes; meantime to failure; Monte Carlo simulation; moving order statistics; multivariate Pareto distribution; Samaniego’s signature;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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