On the Equivalence of Likelihood‐Based Confidence Bands for Fatigue‐Life and Fatigue‐Strength Distributions
Year: 2024
Type: article
Abstract: 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.
DOI: 10.1002/asmb.2911
Institutions: Virginia Tech, Louisiana State University, Iowa State University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,620
OpenAlex ID: W4405687420