Abstract: The present disclosure provides advantageous probabilistic models and applications for component (e.g., titanium component) design optimization, and related methods of use. More particularly, the present disclosure provides advantageous probabilistic models, systems and applications for component design optimization and related methods of use, and where the probabilistic models, systems and applications can accurately predict the life/failure of components (e.g., titanium components) based on material microstructure statistics and/or product mission specifics and/or variations. Disclosed are probabilistic systems and methods for predicting dwell fatigue behavior of a component (e.g., titanium component). The present disclosure advantageously provides an analytical modeling framework that captures the various physics-based mechanisms for dwell fatigue damage accumulation, crack nucleation, crack propagation and fracture in components or materials (e.g., anisotropic components/materials).