This thesis develops improved stochastic models for the description of a large variety of fatigue crack growth phenomena that occur in structural and mechanical components of fundamental importance to the functionality and reliability of complex and modern engineering structures. In essence, the models are based upon the recently available McGill-Markov and the newly developed Closure-Lognormal stochastic processes. These models have not only the capability of predicting the statistical dispersion of the crack growth rate, which is dependent on the inherent crack resistance characteristics of the material being examined, but also, by incorporating the concept of crack closure into the Paris-Erdogan law through the use of the effective stress intensity range factor, have the capability of transferring the stochastic properties of crack growth rates measured under ideal laboratory conditions to situations of industrial significance, such as those occurring under adverse loading and/or environmental conditions.The primary data required in order to be in a position to estimate the pertinent parameters of these stochastic models are obtained, as is fully discussed in this thesis, from a statistically significant number of replicate tests. The application of both the theory and the experimental technique are illustrated using a Ti-6Al-4V alloy of considerable importance to the aerospace industry.The application of these models for the assessment of component reliability is detailed in the latter stages of the investigation reported in this thesis. Important reliability, availability and maintainability concepts are developed and thoroughly illustrated. In this way, fundamental models developed during the course of this investigation will in the future, have the capability of predicting reliability and maintenance parameters of considerable significance to the assessment of component reliability