The design and operation of premixers for gas turbines must deal with the possibility of relatively rare events causing dangerous autoignition. Rare autoignition 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 modelling to increase efficiency and feasibility in premixer design optimisation 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 then reconstructed and solved in a post-processing fashion for each sample, leveraging a well-resolved CFD solution of the non-reacting flow inside the premixer. Via detailed chemistry and reduced computational costs, the evolution of autoignition precursors and temperature, conditioned on a mixture fraction, is tracked, and accurate surrogate models are trained on all samples. The final quantification of the autoignition 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 optimised to maximise system performance while observing a constraint on the allowable probability of autoignition.