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1 results

  • Lower tail analysis of the distribution of the strength of load-sharing systems

  • D. G. Harlow, R. L. Smith, H. M. Taylor
  • Journal:
    Journal of Applied Probability / Volume 20 / Issue 2 / June 1983
    Published online by Cambridge University Press:
    14 July 2016, pp. 358-367
    Print publication:
    June 1983

  • The Weibull distribution for the strength of a long fiber is reviewed, with emphasis on its derivation via extreme-value theory. It is shown that a corresponding Weibull distribution, but with different scale and shape parameters, is appropriate for the lower tail distribution of a bundle of parallel fibers under general load-sharing assumptions. This result is applied to series-parallel systems. The paper contains discussion of the application of these results to the strength of fibrous materials. It is concluded that the Weibull approximation, developed for series-parallel systems, is appropriate for long thin materials consisting of a small number of parallel fibers.