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Estimation of parameters of component lifetime distribution in a coherent system

Author

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  • M. G. Kulkarni

    (Savitribai Phule Pune University)

  • M. B. Rajarshi

    (Savitribai Phule Pune University)

Abstract

We deal with estimation of parameters of lifetime distribution of components which form a coherent system. It is assumed that the system lifetime and the number of failed components up to the moment of the system failure, including the component which fails at the system failure epoch, are observed for each system.We apply the theory of optimal estimating functions and obtain optimal estimators of the parameters assuming that component lifetime has exponential and Weibull distribution. We apply Fisher’s conditionality principle and obtain properties of estimators of the system based on the conditional distribution of the system life-time, given the number of failed components in the system. Exact conditional distributions of the estimators as well as conditional consistency and asymptotic normality have been discussed for both the models. We also compare the proposed estimators with some of the existing estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:1:d:10.1007_s00362-017-0945-1
    DOI: 10.1007/s00362-017-0945-1
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    References listed on IDEAS

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    1. Eryilmaz, Serkan, 2011. "Estimation in coherent reliability systems through copulas," Reliability Engineering and System Safety, Elsevier, vol. 96(5), pages 564-568.
    2. Priebe, Carey E., 2011. "Fisher’s Conditionality Principle in Statistical Pattern Recognition," The American Statistician, American Statistical Association, vol. 65(3), pages 167-169.
    3. 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.
    4. Sigeo Aki & Katuomi Hirano, 1996. "Lifetime distribution and estimation problems of consecutive-k-out-of-n:F systems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(1), pages 185-199, March.
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