On fitting a fatigue model to data

Fatigue lifetimes are dependent on several physical constraints. Therefore, a realistic model for analyzing fatigue lifetime data should take into account these constraints. These physical considerations lead to a functional solution in the form of two five-parameter models for the analysis of fatigue lifetime data. The parameters have clear physical interpretations. However, the standard estimation methods, such as the maximum likelihood, do not produce satisfactory results because: (a) the range of the distribution depends on the parameters, (b) the parameters appear non-linearly in the likelihood gradient equations and hence their solution requires multidimensional searches which may lead to convergence problems, and (c) the maximum likelihood estimates may not exist because the likelihood can be made infinite for some values of the parameters. Castillo and Hadi [5] consider only one of the two models and use the elemental percentile method to estimate the parameters and quantiles. This paper considers the other model. The parameters and quantiles are estimated by the elemental percentile method and are easy to compute. A simulation study shows that the estimators perform well under different values of the parameters. The method is also illustrated by fitting the model to an example of real-life fatigue lifetime data.