Many of the problems we solve involve significant uncertainties in the input variables. This is particularly true for advanced concepts or advanced technologies where new ideas are being exploited. A typical example is the use of an advanced high-temperature ceramic matrix composite material (CMC) such as silicon carbide in a turbine vane application. A traditional deterministic failure analysis concluded that a test specimen undergoing a life verification test would survive unconditionally. But a subsequent probabilistic analysis revealed a significant failure risk due to material property uncertainties. While a turbine vane failure during laboratory testing is not considered catastrophic, such a failure during normal operational usage would be.