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Component importance based on dependence measures

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  • Mario Hellmich

    (Bundesamt für kerntechnische Entsorgungssicherheit (Federal Office for the Safety of Nuclear Waste Management))

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.

Suggested Citation

  • Mario Hellmich, 2018. "Component importance based on dependence measures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(2), pages 229-250, April.
    • Handle: RePEc:spr:mathme:v:87:y:2018:i:2:d:10.1007_s00186-017-0617-x
    DOI: 10.1007/s00186-017-0617-x
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    References listed on IDEAS

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    1. Bent Natvig, 2011. "Measures of Component Importance in Nonrepairable and Repairable Multistate Strongly Coherent Systems," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 523-547, September.
    2. Nader Ebrahimi & Ehsan S. Soofi & Refik Soyer, 2010. "Information Measures in Perspective," International Statistical Review, International Statistical Institute, vol. 78(3), pages 383-412, December.
    3. George Kimeldorf & Allan Sampson, 1989. "A framework for positive dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(1), pages 31-45, March.
    4. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    5. Natvig, Bent, 1979. "A suggestion of a new measure of importance of system components," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 319-330, December.
    6. Marco Scarsini, 1984. "Strong measures of concordance and convergence in probability," Post-Print hal-00542387, HAL.
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