Characteristic parameter values of seismic isolators deviate from their nominal design values dile to uncertainties and/or errors in their material properties and element dimensions, etc. Deviations may increase over service life due to environmental effects and service conditions. For accurate evaluation of the seismic safety level, all such effects, which would result in deviations in the structural response, need to be taken into account In this study, the sensitivity of the probability of failure of the structures equipped with nonlinear base isolation systems to the uncertainties in various isolation system characteristic parameters is investigated in terms of various isolation system and superstructure response parameters in the context of a realistic three-dimensional base-isolated building model via Monte Carlo Simulations. The inherent record-to-record variability nature of the earthquake ground motions is also taken into account by carrying out analyses for a large number of ground motion records which are classified as those with and without forward-directivity effects. Two levels of nominal isolation periods each with three different levels of uncertainty are considered. Comparative plots of cumulative distribution functions and related statistical evaluation presented here portray the potential extent of the deviation of the structural response parameters resulting from the uncertainties and the uncertainty levels considered, which is expected to be useful for practicing engineers in evaluating isolator test results for their projects.