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Asymptotic behavior of the hazard rate in systems based on sequential order statistics

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Abstract

The limiting behavior of the hazard rate of coherent systems based on sequential order statistics is examined. Related results for the survival function of the system lifetime are also considered. For deriving the results, properties of limits involving a relevation transform are studied in detail. Then, limits of characteristics in sequential \(k\)-out-of-\(n\) systems and general coherent systems with failure-dependent components are obtained. Applications to the comparison of different systems based on their long run behavior and to limits of coefficients in a signature-based representation of the residual system lifetime are given.

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Acknowledgments

We thank two referees for helpful comments that significantly improved the presentation of the results. JN is partially supported by Ministerio de Ciencia y Tecnología de España under grant MTM2009-08311 and Fundación Séneca (C.A.R.M.) under grant 08627/PI/08.

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Authors and Affiliations

  1. Institute of Mathematical Stochastics, Otto von Guericke University Magdeburg, 39016 , Magdeburg, Germany

    M. Burkschat

  2. Facultad de Matemáticas, Universidad de Murcia, 30100 , Murcia, Spain

    J. Navarro

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  1. M. Burkschat
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  2. J. Navarro
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Correspondence to M. Burkschat.

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Burkschat, M., Navarro, J. Asymptotic behavior of the hazard rate in systems based on sequential order statistics. Metrika 77, 965–994 (2014). https://doi.org/10.1007/s00184-013-0481-5

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