How do you apply probabilistic methods to aircraft structural analysis?

Probabilistic structural analysis accounts for variability in: Material properties (A-basis, B-basis allowables from statistical distribution), Loads (gust intensity, maneuver probability), Manufacturing variations (thickness, fastener installation), and Inspection capability (POD curves). Methods include: Monte Carlo simulation for complex systems, First/Second Order Reliability Methods (FORM/SORM) for efficiency, Response surface methods for computational tractability, and Bayesian updating with service data. Applications: Risk-based inspection intervals, Reliability-Based Design Optimization (RBDO), fleet management decisions, and Limit of Validity determination. Target reliability levels (~10^-9 per flight hour for catastrophic failure) drive analysis requirements. Certification increasingly accepts probabilistic substantiation with appropriate validation.