SEDL / STP / STP1201-EB / STP12786S

Weibull Estimators for Pooled Fracture Data

Johnson, CA
Ceramist and statistician, General Electric Company, Corporate Research and Development, Schenectady, NY

Tucker, WT
Ceramist and statistician, General Electric Company, Corporate Research and Development, Schenectady, NY

Pages: 15    Published: Jan 1994

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Abstract

An 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 of 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 extract information of all three types from the data to yield the best overall estimates of distribution parameters and fracture strengths. Two Weibull estimators for pooled fracture data are derived and discussed. One is based on linear regression and the other on the maximum likelihood technique. The pooled estimators are extensions of conventional linear regression and maximum likelihood estimators. The estimators are derived for the two-parameter, size-scaled, uniaxial Weibull distribution function. It has been shown, however, that these estimators are also valid for multiaxial Weibull models. The pooled estimators are demonstrated using strength data from sintered SiC tested in six different combinations of specimen size and bending configuration.