Chapter 46. Weibull Estimators for Pooled Fracture Data

  1. John B. Wachtman Jr.
  1. Curtis A. Johnson and
  2. William T. Tucker

Published Online: 28 MAR 2008

DOI: 10.1002/9780470314180.ch46

Proceedings of the 17th Annual Conference on Composites and Advanced Ceramic Materials, Part 1 of 2: Ceramic Engineering and Science Proceedings, Volume 14, Issue 7/8

Proceedings of the 17th Annual Conference on Composites and Advanced Ceramic Materials, Part 1 of 2: Ceramic Engineering and Science Proceedings, Volume 14, Issue 7/8

How to Cite

Johnson, C. A. and Tucker, W. T. (2008) Weibull Estimators for Pooled Fracture Data, in Proceedings of the 17th Annual Conference on Composites and Advanced Ceramic Materials, Part 1 of 2: Ceramic Engineering and Science Proceedings, Volume 14, Issue 7/8 (ed J. B. Wachtman), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470314180.ch46

Author Information

  1. General Electric Corporate Research and Development, Schenectady, NY 12301

Publication History

  1. Published Online: 28 MAR 2008
  2. Published Print: 1 JAN 1993

ISBN Information

Print ISBN: 9780470375266

Online ISBN: 9780470314180

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Keywords:

  • algorithm;
  • analyze;
  • parameters;
  • efficiency;
  • quantitatively

Summary

A Weibull estimator is a method or algorithm to analyze fracture data and estimate useful quantities such as distribution parameters and predicted component strengths. There are advantages in efficiency and model validation that typically result from combining or pooling fracture data from multiple specimen sizes and geometries. Three types of information are contained in pooled data sets: variability in strength within subgroups, dependence of strength on specimen size, and dependence of strength on loading geometry. Efficient pooled estimators use all three types of information to yield the best overall estimates of distribution parameters and fracture strengths. As mentioned above, pooled estimators also allow model validation. Size-scaling aspects of the Weibull model can be quantitatively tested using pooled data sets that include specimens with multiple specimen sizes and/or geometries.

This paper describes two Weibull estimators for pooled fracture data. One is based on the maximum likelihood technique and the other on linear regression. The pooled estimators are extensions of conventional maximum likelihood and linear regression estimators. Each pooled estimator will be derived and contrasted with the associated conventional estimator. The estimators will be derived for the two-parameter, size-scaled, uniaxial Weibull distribution function. It has been shown, however, that the estimators are also valid for multiaxial Weibull models. The pooled estimators will be demonstrated using strength data from GE boron-doped sintered SiC tested in six bending configurations. The six bending configurations include the A, B, and C specimen geometries of the MIL-STD-1942MR testing standard (virtually identical to ASTM Standard CI 161, adopted in September 1990) where each geometry was tested in both 3-point and 4-point bending.