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Copulae in Reliability Theory (Order Statistics, Coherent Systems)

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Copula Theory and Its Applications

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 198))

Abstract

We discuss useful representations of lifetime distributions of coherent systems by means of convex combinations of marginal distributions of order statistics based on the lifetimes of exchangeable components. The representations are applied for characterizing distributions of system lifetimes composed of exchangeable units with given marginal distribution and joint absolutely continuous copula. The characterizations are used for calculating sharp bounds on the expectations and variancesof system lifetimes by means of respective parameters of single unit lifetime distribution.

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Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Toruń, Poland

    Tomasz Rychlik

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  1. Tomasz Rychlik
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Correspondence to Tomasz Rychlik .

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Editors and Affiliations

  1. , Faculty of Mathematics Informatics, University of Warsaw, ul. Banacha 2, Warszawa, 02097, Poland

    Piotr Jaworski

  2. , Department of Knowledge-Based, Johannes Kepler Universität, Altenberger Straße 69, Linz, 4040, Austria

    Fabrizio Durante

  3. Ladislaus von Bortkiewicz Chair of Stati, C.A.S.E. Centre for Applied Statistics a, Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

  4. , Mathematical Institute, Polish Academy of Sciences, ul. Chopina 12, Toruń, 87100, Poland

    Tomasz Rychlik

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Rychlik, T. (2010). Copulae in Reliability Theory (Order Statistics, Coherent Systems). In: Jaworski, P., Durante, F., Härdle, W., Rychlik, T. (eds) Copula Theory and Its Applications. Lecture Notes in Statistics(), vol 198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12465-5_9

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