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

Published online by Cambridge University Press:  14 July 2016

D. G. Harlow ,
R. L. Smith  and
H. M. Taylor
D. G. Harlow
Affiliation:
Drexel University
R. L. Smith*
Affiliation:
Imperial College, London
H. M. Taylor*
Affiliation:
Cornell University
*
∗∗ Postal address: Department of Mathematics, Imperial College of Science and Technology, Huxley Building, Queen's Gate, London SW7 2BZ, U.K.
∗∗∗ Postal address: School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, U.S.A.
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Abstract

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.

Keywords

BUNDLES OF FIBERSWEIBULL FAILURE LAWSERIES–PARALLEL SYSTEMSSIZE EFFECTEXTREME-VALUE THEORY
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 358 - 367
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

∗)

Present address: Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, U.S.A.

Research supported in part by the National Science Foundation under Grant ENG 75-00570.

References

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