Empirical Confidence Bounds  
Author D. Gary Harlow




Abstract The uncertainty is unavoidable in the design of engineered systems, components, and structural materials subjected to complex loading. For fatigue life, uncertainty is a combination of variability in experimentation due to material and loading variability, in manufacturing processing, and in imprecise scientific modeling. Thus, uncertainty cannot be ignored. The impact of uncertainty is exacerbated for high reliability applications. One of the ways to estimate the effect of uncertainty is to consider confidence bounds for cumulative distribution functions associated with life. The purpose of this paper is to investigate the statistical variability and appropriately model that variability. Illustrations are taken from examples of fatigue life. A variety of statistical methods are used to estimate confidence bounds, including mean square error, mean absolute error, Dvoretzky-Kiefer- Wolfowitz, and pointwise Normal approximation methods. Since high reliability and long life is typically desired, the emphasis will be placed on the behavior in the lower tails of the distribution functions. Data for creep strengthened 9Cr- 1Mo steel will be used as examples.


Keywords Dvoretzky-Kiefer-Wolfowitz Bounds, Fatigue Life, Mean Absolute Error Analysis, Mean Square Error Analysis, Pointwise Normal Approximation Bounds, Weibull distribution
    Article #:  23-015
Proceedings of the 23rd ISSAT International Conference on Reliability and Quality in Design
August 3-5, 2017 - Chicago, Illinois, U.S.A.