  Efficiently approximating the probability of system failure has gained
increasing importance as expensive simulations begin to play a larger role in
reliability quantification tasks in areas such as structural design, power grid
design, and safety certification among others. This work derives credible
intervals on the probability of failure for a simulation which we assume is a
realizations of a Gaussian process. We connect these intervals to binary
classification error and comment on their applicability to a broad class of
iterative schemes proposed throughout the literature. A novel iterative
sampling scheme is proposed which can suggest multiple samples per batch for
simulations with parallel implementations. We empirically test our scalable,
open-source implementation on a variety simulations including a Tsunami model
where failure is quantified in terms of maximum wave hight.
