Parameter and quantile estimation for a fatigue model

In Castillo and Hadi (1995), a new model for the analysis of lifetime data in the presence of a covariate is presented. The model is derived based on physical and statistical considerations. Two methods for the estimation of these parameters were also presented in the paper. These methods are lacking however since not all collected data are involved in the fitting. In this paper, new methods are constructed to consider all points in the estimation procedure. Furthermore, as fatigue data is susceptible to mishandled observations, it is important that estimation methods show robustness. The proposed methods were also built with the latter in mind. A simulation study shows that the new methods perform better, especially in presence of contamination. The new methodology is illustrated on fatigue data on concrete.