Systems with Exchangeable Components and Gumbel Exponential Distribution

  • Jorge Navarro
  • Jose M. Ruiz
  • Carlos J. Sandoval
Part of the Statistics for Industry and Technology book series (SIT)


The life lengths of some possibly dependent components in a system can be modelled by a multivariate distribution. In this paper, we suppose that the joint distribution of the units is a symmetric multivariate Gumbel exponential distribution (GED). Hence, the components are exchangeable and have exponential (marginal) distributions. For this model, we obtain basic reliability properties for k-out-of-n systems (order statistics) and, in particular, for series and parallel systems. We pay special attention to systems with two components. Some results are extended to coherent systems with n exchangeable components.

Keywords and phrases

Reliability failure rate mean residual life k-out-of-n systems coherent systems order statistics 


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Copyright information

© Birkhäuser Boston 2006

Authors and Affiliations

  • Jorge Navarro
    • 1
  • Jose M. Ruiz
    • 1
  • Carlos J. Sandoval
    • 2
  1. 1.Universidad de MurciaMurciaSpain
  2. 2.Universidad Catolica San Antonio de MurciaMurciaSpain

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