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Estimation of a Minimum Allowable Structural Strength Based on Uncertainty in Material Test Data



Jeffrey Fong, N. Alan Heckert, James J. Filliben, Pedro V. Marcal, Stephen W. Freiman


Three types of uncertainties exist in the estimation of the minimum fracture strength of a full-scale component or structure size. The first, to be called the "model selection uncertainty," is in selecting a statistical distribution that best fits the laboratory test data. The second, to be called the "laboratory-scale strength uncertainty," is in estimating model parameters of a specific distribution from which the minimum failure strength of a material at a certain confidence level is estimated using the laboratory test data. To extrapolate the laboratory-scale strength prediction to that of a full-scale component, a third uncertainty exists that can be called the "full-scale strength uncertainty." In this paper, we develop a three-step approach to estimating the minimum strength of a full-scale component using two metrics: One metric is based on six goodness-of-fit and parameter-estimation-method criteria, and the second metric is based on the uncertainty quantification of the so-called A-basis design allowable (99 % coverage at 95 % level of confidence) of the full-scale component. The three steps of our approach are: (1) Find the "best" model for the sample data from a list of five candidates, namely, normal, two-parameter Weibull, three-parameter Weibull, two-parameter lognormal, and three-parameter lognormal. (2) For each model, estimate (2a) the parameters of that model with uncertainty using the sample data, and (2b) the minimum strength at the laboratory scale at 95 % level of confidence. (3) Introduce the concept of "coverage" and estimate the fullscale allowable minimum strength of the component at 95 % level of confidence for two types of coverages commonly used in the aerospace industry, namely, 99 % (A-basis for critical parts) and 90 % (B-basis for less critical parts). This uncertainty-based approach is novel in all three steps: In step-1 we use a composite goodness-of-fit metric to rank and select the "best" distribution, in step-2 we introduce uncertainty quantification in estimating the parameters of each distribution, and in step-3 we introduce the concept of an uncertainty metric based on the estimates of the upper and lower tolerance limits of the so-called A-basis design allowable minimum strength. To illustrate the applicability of this uncertainty-based approach to a diverse group of data, we present results of our analysis for six sets of laboratory failure strength data from four engineering materials. A discussion of the significance and limitations of this approach and some concluding remarks are included.
Journal of Research (NIST JRES) -


aluminum oxide, Anderson-Darling criterion, ASTM C1239-07, borosilicate crown BK-7 glass, chi-square criterion, DATAPLOT, failure strength test, goodness-of-fit, high-strength steels, Kolmogorov-Smirnov criterion, lognormal, maximum likelihood method, model selection, normal, probability plot correlation coefficient, probability plot correlation coefficient criterion, silicon nitride, statistical data analysis, structural reliability, uncertainty quantification, Weibull distribution


Fong, J. , Heckert, N. , Filliben, J. , Marcal, P. and Freiman, S. (2021), Estimation of a Minimum Allowable Structural Strength Based on Uncertainty in Material Test Data, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed May 27, 2024)


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Created December 7, 2021