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Efficiently approximating the probability of system failure has gainedincreasing importance as expensive simulations begin to play a larger role inreliability quantification tasks in areas such as structural design, power griddesign, and safety certification among others. This work derives credibleintervals on the probability of failure for a simulation which we assume is arealizations of a Gaussian process. We connect these intervals to binaryclassification error and comment on their applicability to a broad class ofiterative schemes proposed throughout the literature. A novel iterativesampling scheme is proposed which can suggest multiple samples per batch forsimulations with parallel implementations. We empirically test our scalable,open-source implementation on a variety simulations including a Tsunami modelwhere failure is quantified in terms of maximum wave hight.

Credible Intervals for Probability of Failure with Gaussian Processes