"Preface The subject of fatigue degradation and methodologies for its treatment spans multitudes of scientific disciplines ranging from engineering to materials science, and from mechanics to mathematics. Fatigue is probabilistic in nature. For example, fatigue tests performed on the same material subjected to the same operating conditions can yield different results in terms of the number of cycles that the system can withstand before failure occurs. Such uncertainties affect the system design, its structural integrity, and operational reliability. Yet the majority of available methods for prediction of fatigue failure--such as cumulative damage models, cyclic plastic energy hypothesis, crack propagation rate models, and empirically-derived relationships based on the curve fitting of the limited laboratory data--are based on deterministic- type theories and their applications require many unknown input parameters that must be experimentally determined. There are other complications. All of the above-mentioned methods concentrate on very specific types of loading and single fatigue modes, that is, bending, or torsion, or tensioncompression. In practice, however, fatigue involves simultaneous interaction of multimode processes. Further, the variability inthe duty cycle in practical applications may render many of these existing methods incapable of reliable prediction. It is, therefore, no surprise that the application of these theories often leads to many uncertainties in the design. Further, their use and execution in practice requires one to implement large factors of safety, often leading to gross overdesigns that waste resources and cost more"--