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The Estimation of Reliability from Stress–Strength for Exponentiated Frechet Distribution

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Abstract

This paper deals with the problem of estimation of the stress–strength function \(R = P(Y < X)\), when X and Y are two independent but not identically distributed random variables belonging to the exponentiated Frechet (EF) distribution. Different estimators of R, namely, maximum likelihood, uniformly minimum variance unbiased, and Bayes, are derived in closed form. In addition, two-sided confidence interval for R is obtained. We discuss the reliability in multi-component model. Simulation studies are performed to compare the different estimates of \(R\) and \(R_{s, k}\). Real data are used as a practical application of the proposed procedure.

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Acknowledgements

The authors are deeply thankful to the two reviewers and Editor for their valuable suggestions which really improve the quality of the manuscript.

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Authors and Affiliations

  1. Statistics Department, Faculty of Science for Girls, King Abdulaziz University, P. O. Box 70973, Jeddah, 21577, Saudi Arabia

    M. M. Badr

  2. Statistics Department, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia

    A. I. Shawky & A. H. Alharby

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  1. M. M. Badr
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  2. A. I. Shawky
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  3. A. H. Alharby
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Correspondence to M. M. Badr.

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Badr, M.M., Shawky, A.I. & Alharby, A.H. The Estimation of Reliability from Stress–Strength for Exponentiated Frechet Distribution. Iran J Sci Technol Trans Sci 43, 863–874 (2019). https://doi.org/10.1007/s40995-017-0372-0

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  • DOI: https://doi.org/10.1007/s40995-017-0372-0

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