Comparison of prediction intervals for crack growth based on random effects models

Abstract

Linear and nonlinear mixed effects models are applied extensively in the study of repeated measurements and longitudinal data. In this thesis, we propose two linear random effects models and a nonlinear random effects model based on the Paris-Erdogan equation for describing the crack growth data of Virkler et al. (1979). We describe how such models can be applied to achieve the future prediction and prediction interval of the time, when the crack attains a specific length. We propose eleven new methods for prediction interval by extending the methods of Swamy (1971), Rao (1975), Liski and Nummi (1996), Pinheiro and Bates (2000) and Stirnemann et al. (2011). We compare the methods and models by applying them on the crack propagation and simulated data.