Planning fatigue experiments and analyzing fatigue data with the random fatigue-limit model and modified sudden death tests

Abstract

In a fatigue-limit model, test units tested below the fatigue limit (also known as the threshold stress) theoretically will never fail. This paper 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 fit the model to actual fatigue data sets by maximum likelihood methods and study the fits under different distributional assumptions. The 0.01 and 0.05 quantiles of the life distribution are often of interest to designers. Lower confidence bounds based on likelihood-ratio methods are obtained for these quantiles. To assess the fits of the model, we construct diagnostic plots and perform goodness-of-fit tests and residual analyses.