CONFIDENCE BOUNDS FOR FATIGUE DISTRIBUTION FUNCTIONS

The effect of uncertainty is critical in the design of complex engineered systems, components, and structural materials subjected to fatigue. Uncertainty in fatigue life prediction is a combination of several factors. In fact, it cannot be eliminated from experimentation due to material and loading variability, manufacturing processing, and imprecise scientific modeling. Consequently, uncertainty must be characterized and managed. The impact of uncertainty is exacerbated especially when high reliability must be assured. One of the ways to estimate the effect of uncertainty is to consider confidence bounds for fatigue life prediction, specifically, for cumulative distribution functions associated with life. The purpose of this paper is to investigate the statistical variability and appropriately model that variability for life in fatigue using appropriate cumulative distribution functions, and subsequently, evaluate a variety of statistical methods to estimate confidence bounds. Specifically, the confidence bounds will be estimated using mean square error, Dvoretzky-Kiefer-Wolfowitz, and pointwise Normal approximation methods. Since high reliability and long life is typically desired, extra emphasis will be placed on estimation in the lower tails of the distribution functions. The ensuing analyses are based on data for a cold-rolled, low carbon, extra deep drawing steel, ASTM A969, and creep strengthened 9Cr-1Mo steel.