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Reliability Estimation in Load-Sharing System Model with Application to Real Data

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Abstract

This study deals with the reliability analysis of a multi-component load sharing system where failure of any component within the system induces higher failure rate on the remaining surviving components. It is assumed that each component failure time follows Chen distribution. In classical set up, the maximum likelihood estimates of the load sharing parameters, system reliability and hazard rate along with their standard errors are computed. Since maximum likelihood estimates are not in closed form, so asymptotic confidence intervals and two bootstrap confidence intervals for the unknown parameters have also been constructed. Further, by assuming both informative and non-informative prior for the unknown parameters, Bayes estimates along with their posterior standard errors and HPD intervals of the parameters are obtained. Thereafter, a simulation study elicitates the theoretical developments. A real data analysis, at the end, eshtablishes the applicability of the proposed theory.

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Acknowledgements

The authors gratefully acknowledge the critical suggestions and comments from the learned referee which greatly helped us in the improvement of this paper.

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Authors and Affiliations

  1. Department of Statistics, University of Allahabad, Allahabad, 211 002, India

    Pramendra Singh Pundir & Puneet Kumar Gupta

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  1. Pramendra Singh Pundir
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  2. Puneet Kumar Gupta
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Correspondence to Puneet Kumar Gupta.

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Pundir, P.S., Gupta, P.K. Reliability Estimation in Load-Sharing System Model with Application to Real Data. Ann. Data. Sci. 5, 69–91 (2018). https://doi.org/10.1007/s40745-017-0120-5

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  • DOI: https://doi.org/10.1007/s40745-017-0120-5

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