  Fatigue data arise in many research and applied areas and there have been
statistical methods developed to model and analyze such data. The distributions
of fatigue life and fatigue strength are often of interest to engineers
designing products that might fail due to fatigue from cyclic-stress loading.
Based on a specified statistical model and the maximum likelihood method, the
cumulative distribution function (cdf) and quantile function (qf) can be
estimated for the fatigue-life and fatigue-strength distributions.
Likelihood-based confidence bands then can be obtained for the cdf and qf. This
paper provides equivalence results for confidence bands for fatigue-life and
fatigue-strength models. These results are useful for data analysis and
computing implementation. We show (a) the equivalence of the confidence bands
for the fatigue-life cdf and the fatigue-life qf, (b) the equivalence of
confidence bands for the fatigue-strength cdf and the fatigue-strength qf, and
(c) the equivalence of confidence bands for the fatigue-life qf and the
fatigue-strength qf. Then we illustrate the usefulness of those equivalence
results with two examples using experimental fatigue data.
