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Non-parametric prediction intervals for the lifetime of coherent systems

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  • M. Chahkandi
  • Jafar Ahmadi
  • S. Baratpour

Abstract

In this paper, nonparametric methods are proposed to construct prediction intervals for the lifetime of a coherent system with known signatures. An explicit expression for the coverage probability of the prediction intervals is presented based on Samaniego’s signature. The existence and optimality of these intervals are discussed. In our derivation, we also obtain an exact expression for the marginal distribution of the $$i$$ i th order statistic from a pooled sample. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • M. Chahkandi & Jafar Ahmadi & S. Baratpour, 2014. "Non-parametric prediction intervals for the lifetime of coherent systems," Statistical Papers, Springer, vol. 55(4), pages 1019-1034, November.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:4:p:1019-1034
    DOI: 10.1007/s00362-013-0549-3
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    References listed on IDEAS

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    1. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    2. Eryilmaz, Serkan, 2011. "Estimation in coherent reliability systems through copulas," Reliability Engineering and System Safety, Elsevier, vol. 96(5), pages 564-568.
    3. Hon Ng & Jorge Navarro & Narayanaswamy Balakrishnan, 2012. "Parametric inference from system lifetime data under a proportional hazard rate model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(3), pages 367-388, April.
    4. Nakagawa, Toshio & Kowada, Masashi, 1983. "Analysis of a system with minimal repair and its application to replacement policy," European Journal of Operational Research, Elsevier, vol. 12(2), pages 176-182, February.
    5. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, April.
    6. Narayanaswamy Balakrishnan & Hon Ng & Jorge Navarro, 2011. "Exact nonparametric inference for component lifetime distribution based on lifetime data from systems with known signatures," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 741-752.
    7. Navarro, Jorge & Rychlik, Tomasz, 2007. "Reliability and expectation bounds for coherent systems with exchangeable components," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 102-113, January.
    8. S. Gurler, 2012. "On residual lifetimes in sequential (n − k + 1)-out-of-n systems," Statistical Papers, Springer, vol. 53(1), pages 23-31, February.
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    Cited by:

    1. Jingjing Qu & Hon Keung Tony Ng & Chul Moon, 2024. "Empirical likelihood ratio tests for homogeneity of component lifetime distributions based on system lifetime data," Computational Statistics, Springer, vol. 39(6), pages 3007-3029, September.
    2. M. G. Kulkarni & M. B. Rajarshi, 2020. "Estimation of parameters of component lifetime distribution in a coherent system," Statistical Papers, Springer, vol. 61(1), pages 403-421, February.

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