In the paper, we evaluate the reliability of a successful evacuation using a CFD fire simulation tool and an evacuation model. Obviously, it is not possible to perform Monte Carlo analysis in a reasonable amount of time because of the high computational costs. Hence, we utilize an adaptive response surface method based on moving least squares in order to compute the reliability. To further decrease the necessary number of numerical evaluations, a preceding sensitivity analysis yields information about the variance of the results and the relevance of the input parameters and hence helps to identify a surrogate model of optimal prognosis. The preliminary scan of the random space for the sensitivity analysis can also be used to obtain information about the approximate location of the design point so that further support points can be concentrated in this relevant area. Using this information for the subsequent reliability analysis leads to a faster convergence. The methodology described will be utilized to evaluate the reliability of a typical example in fire protection engineering.