Engineers and scientists have been collecting and analyzing fatigue data
since the 1800s to ensure the reliability of life-critical structures.
Applications include (but are not limited to) bridges, building structures,
aircraft and spacecraft components, ships, ground-based vehicles, and medical
devices. Engineers need to estimate S-N relationships (Stress or Strain versus
Number of cycles to failure), typically with a focus on estimating small
quantiles of the fatigue-life distribution. Estimates from this kind of model
are used as input to models (e.g., cumulative damage models) that predict
failure-time distributions under varying stress patterns. Also, design
engineers need to estimate lower-tail quantiles of the closely related
fatigue-strength distribution. The history of applying incorrect statistical
methods is nearly as long and such practices continue to the present. Examples
include treating the applied stress (or strain) as the response and the number
of cycles to failure as the explanatory variable in regression analyses
(because of the need to estimate strength distributions) and ignoring or
otherwise mishandling censored observations (known as runouts in the fatigue
literature). The first part of the paper reviews the traditional modeling
approach where a fatigue-life model is specified. We then show how this
specification induces a corresponding fatigue-strength model. The second part
of the paper presents a novel alternative modeling approach where a
fatigue-strength model is specified and a corresponding fatigue-life model is
induced. We explain and illustrate the important advantages of this new
modeling approach.Comment: 93 pages, 27 page