A critical comparison of two models for assessment of fatigue data

A comparison and a critical discussion of the results obtained for the analysis of fatigue data using the up-and-down method and the Wöhler field based method proposed by Castillo et al. are done and some practical conclusions are given. In addition, the paper introduces an alternative Markov model for analyzing the up-and-down method which improves that proposed by Chao and Fuh [Chao MT, Fuh CD. Bootstrap methods for the up and down test on pyrotechnics sensitivity analysis. Stat Sinica 2001; 1–21.] in that it keeps one of the characteristic features of the up-and-down method consisting of the fact that some stress levels are not possible for odd steps and some are not possible for even steps. In addition, the method is valid for any parent distribution including the most common normal and Weibull models. In particular the case of a Weibull parent distribution is used for fatigue data and two estimation methods are presented: maximum likelihood and least squares. In particular, it is shown that the up-and-down method neglects important information contained in the data making it very expensive and inefficient when compared with other alternative models. The methods are illustrated using data from Dixon and Mood and an experimental program carried out at Empa.