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Engineering Risk in Natural Resources Management pp 149–158Cite as

Some Reliability Measures for Nonstationary Markov Chains

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Part of the book series: NATO ASI Series ((NSSE,volume 275))

Abstract

A general survey of reliability and resilience related definitions found in the reliability literature as well as in the water resources literature is presented. The measures presented are general and may be adapted to specific problems. Often, systems are modeled as stationary Markov chains with constant hazard rates, which is not always a realistic assumption, especially under changing climatic conditions. In this paper, the pointwise availability, reliability function, average availability, conditional expected number of failures and restorations in a time interval are derived for the case where the system is a nonstationary continuous-time Markov chain. The nonstationarity is modeled by transition rates that are linear with respect to time.

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Author information

Authors and Affiliations

  1. INRS-Eau, 2800 rue Einstein, Québec (Québec), G1V4C7, Canada

    Irène Abi-Zeid & Bernard Bobée

Authors
  1. Irène Abi-Zeid
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  2. Bernard Bobée
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Editor information

Editors and Affiliations

  1. Systems and Industrial Engineering, The University of Arizona, Tucson, Arizona, USA

    L. Duckstein

  2. Department of Applied Mathematics, French Institute of Forestry, Agricultural and Environmental Engineering, Paris, France

    E. Parent

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© 1994 Springer Science+Business Media Dordrecht

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Abi-Zeid, I., Bobée, B. (1994). Some Reliability Measures for Nonstationary Markov Chains. In: Duckstein, L., Parent, E. (eds) Engineering Risk in Natural Resources Management. NATO ASI Series, vol 275. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8271-1_8

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  • DOI: https://doi.org/10.1007/978-94-015-8271-1_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4441-9

  • Online ISBN: 978-94-015-8271-1

  • eBook Packages: Springer Book Archive

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