The design and operation of premixers for gas turbines must deal with the possibility of relatively rare events causing dangerous autoignition (AI). Rare AI events may occur in the presence of fluctuations of operational parameters, such as temperature and fuel composition, and must be understood and predicted. This work presents a methodology based on incompletely stirred reactor (ISR) and surrogate modeling to increase efficiency and feasibility in premixer design optimization for rare events. For a representative premixer, a space-filling design is used to sample the variability of three influential operational parameters. An ISR is reconstructed and solved in a postprocessing fashion for each sample, leveraging a well-resolved computational fluid dynamics solution of the non-reacting flow inside the premixer. Via detailed chemistry and reduced computational costs, ISR tracks the evolution of AI precursors and temperature conditioned on a mixture fraction. Accurate surrogate models are then trained for selected AI metrics on all ISR samples. The final quantification of the AI probability is achieved by querying the surrogate models via Monte Carlo sampling of the random parameters. The approach is fast and reliable so that user-controllable, independent variables can be optimized to maximize system performance while observing a constraint on the allowable probability of AI.