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


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


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.

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  • 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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    References listed on IDEAS

    1. Nadeem Ul Haque & Manmohan S. Kumar & Nelson Mark & Donald J. Mathieson, 1996. "The Economic Content of Indicators of Developing Country Creditworthiness," IMF Staff Papers, Palgrave Macmillan, vol. 43(4), pages 688-724, December.
    2. Rossini Miñán, Renzo, 2001. "Aspectos de la adopción de un régimen de metas de inflación en el Perú," Revista Estudios Económicos, Banco Central de Reserva del Perú, issue 7.
    3. Lama, Ruy, 2002. "Administración del riesgo cambiario en el sistema bancario peruano," Revista Estudios Económicos, Banco Central de Reserva del Perú, issue 8, pages 155-181.
    4. Richard Cantor & Frank Packer, 1996. "Determinants and impact of sovereign credit ratings," Economic Policy Review, Federal Reserve Bank of New York, issue Oct, pages 37-53.
    5. Jiménez Sotelo, Renzo, 2001. "Perú: Una economía estrangulada por el descalce entre la dolarización de los pasivos financieros y la solarización del poder adquisitivo de sus agentes económicos
      [Peru: An economy strangled by the
      ," MPRA Paper 26615, University Library of Munich, Germany, revised 31 Dec 2001.
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    Cited by:

    1. Makri, Frosso S., 2011. "Minimum and maximum distances between failures in binary sequences," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 402-410, March.
    2. repec:eee:reensy:v:95:y:2010:i:3:p:247-254 is not listed on IDEAS
    3. 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.
    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


    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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