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Component importance based on dependence measures

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Abstract

We discuss the construction of component importance measures for binary coherent reliability systems from known stochastic dependence measures by measuring the dependence between system and component failures. We treat both the time-dependent case in which the system and its components are described by binary random variables at a fixed instant as well as the continuous time case where the system and component life times are random variables. As dependence measures we discuss covariance and mutual information, the latter being based on Shannon entropy. We prove some basic properties of the resulting importance measures and obtain results on importance ordering of components.

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Acknowledgements

Thanks are due to the referees whose comments led to a significant improvement of the paper.

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Authors and Affiliations

  1. Bundesamt für kerntechnische Entsorgungssicherheit (Federal Office for the Safety of Nuclear Waste Management), Willy-Brandt-Straße 5, 38226, Salzgitter, Germany

    Mario Hellmich

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  1. Mario Hellmich
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Correspondence to Mario Hellmich.

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Hellmich, M. Component importance based on dependence measures. Math Meth Oper Res 87, 229–250 (2018). https://doi.org/10.1007/s00186-017-0617-x

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  • DOI: https://doi.org/10.1007/s00186-017-0617-x

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