On the Equivalence of Likelihood‐Based Confidence Bands for Fatigue‐Life and Fatigue‐Strength Distributions

ABSTRACT 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 can then 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.