Estimating Fatigue Curves With the Random Fatigue-Limit Model

In a fatigue-limit model, units tested below the fatigue limit (also known as the threshold stress) theoretically will never fail. This article uses a random fatigue-limit model to describe (a) the dependence of fatigue life on the stress level, (b) the variation in fatigue life, and (c) the unit-to-unit variation in the fatigue limit. We t the model to actual fatigue data sets by maximum likelihood methods and study the ts under di erent distributional assumptions. Small quantiles of the life distribution are often of interest to designers. Lower con dence bounds based on likelihood ratio methods are obtained for such quantiles. To assess the ts of the model, we construct diagnostic plots and perform goodness-oft tests and residual analyses.