A different approach to the problem of estimating the strength distribution of brittle fibers is proposed. The procedure assumes a Poisson flaw model, but rather than presum ing a particular functional form, it is assumed that the probability distribution of strength has an increasing failure rate (IFR). The maximum likelihood estimate of the fiber strength distribution is obtained within the class of all distributions with the IFR property, yielding a continuous distribution estimate which is a good fit to fiber tensile strength data, typically fitting much better than the usual Weibull model. The method is illustrated with carbon fiber data.
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References
1.
Bader, M.G. and A.M. Priest. "Statistical Aspects of Fibre and Bundle Strength in Hybrid Composites," Progress in Science and Engineering of Composites, T. Hayashi, K. Kawata & S. Umekawa , eds., ICCM-IV, Tokyo (1982).
2.
Barlow, R.E., D.J. Bartholomew, J.M. Bremner and H.D. Brunk.Statistical Inference Under Order Restrictions, New York:John Wiley and Sons (1972 ).
3.
Barlow, R.E. and F. Proschan.Statistical Theory of Reliability and Life Testing, Probability Models, New York:Holt, Rinehart and Winston (1975).
4.
Harlow, D.G. , R.L. Smith and H.M. Taylor. "Lower Tail Analysis of the Distribution of the Strength of Load-Sharing Systems," Journal of Applied Probability, 20358-367 (1983).
5.
Marshall, A.W. and F. Proschan. "Maximum Likelihood Estimation for Distributions with Monotone Failure Rate," Annals of Mathematical Statistics , 36:69-77 (1965).
6.
Metcalf, A.G. and G.K. Schmitz. "Effect of Length on the Strength of Glass Fibers," Proceedings ASTM, 1075-1093 (1964 ).
7.
Scop, P.M. and A.S. Argon. "Statistical Theory of Strength of Laminated Composites ," Journal of Composite Materials, 1:92-99 (1967).
8.
Wagner, H.D. , S.L. Phoenix and P. Schwartz. "A Study of Statistical Variability in the Strength of Single Aramid Filaments," Journal of Composite Materials, 18:312-338 (1984).
9.
Whitney, W. and R.M. Kimmel. "Griffith Equation and Carbon Fibre Strength," Nature Physical Science, 237:93-94 (1972).
