Gate oxide breakdown is a major cause of reliability failures in future nanometer-scale CMOS designs. This paper develops an analysis technique that can predict the probability of a functional failure in a large digital circuit due to this phenomenon. Novel features of the method include its ability to account for the inherent resilience in a circuit to a breakdown event, while simultaneously considering the impact of process variations. Based on standard process variation models, at a specified time instant, this procedure determines the circuit failure probability as a lognormal distribution. Experimental results demonstrate this approach is accurate compared with Monte Carlo simulation, and gives 4.7-5.9x better lifetime prediction over existing methods that are based on pessimistic area-scaling models.