Estimating Fatigue Curves With the Random Fatigue-Limit Model.

Editor's Note: This article and accompanying discussion were presented orally at the Technometrics Invited Paper Session at the Sixth Annual Spring Research Conference, held in Minneapolis, Minnesota, June 2-4, 1999. This conference is cosponsored by the American Statistical Association and the Institute of Mathematical Statistics.

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 fit the model to actual fatigue datasets by maximum likelihood methods and study the fits under different distributional assumptions. Small quantiles of the life distribution are often of interest to designers. Lower confidence bounds based on likelihood ratio methods are obtained for such quantiles. To assess the fits of the model, we construct diagnostic plots and perform goodness-of-fit tests and residual analyses.

KEY WORDS: Akaike information criterion; Fatigue data; Maximum likelihood methods; Probability (P-P) plots; Random fatigue limit; Right censoring.

1. INTRODUCTION

1.1 Background

The relationship between fatigue life of metal, ceramic, and composite materials and applied stress is an important input to design-for-reliability processes. This article suggests a practical model to describe the relationship between fatigue life and applied stress and provides and illustrates corresponding data-analysis methods. This work is motivated by the need to develop and present quantitative fatigue-life information used in the design of jet engines.

Fatigue data are often presented in the form of a median S-N curve, a log-log plot of cyclic stress or strain s versus the median fatigue life N, which is expressed in cycles to failure. An extension of this concept is the p-quantile S-N curves, also called S-N-P curves, a generalization that relates the p quantile of fatigue life to the applied stress or strain. Thus, each curve represents a constant probability of failure p, as a function of s. We shall use the .05 and .95-quantile S-N curves to illustrate the variability of fatigue life. Unless otherwise specified, the S-N curve in the literature generally refers to the median curve. We shall use the S-N curve as such.