  Estimating probability of failure in aerospace systems is a critical
requirement for flight certification and qualification. Failure probability
estimation involves resolving tails of probability distribution, and Monte
Carlo sampling methods are intractable when expensive high-fidelity simulations
have to be queried. We propose a method to use models of multiple fidelities
that trade accuracy for computational efficiency. Specifically, we propose the
use of multifidelity Gaussian process models to efficiently fuse models at
multiple fidelity, thereby offering a cheap surrogate model that emulates the
original model at all fidelities. Furthermore, we propose a novel sequential
\emph{acquisition function}-based experiment design framework that can
automatically select samples from appropriate fidelity models to make
predictions about quantities of interest in the highest fidelity. We use our
proposed approach in an importance sampling setting and demonstrate our method
on the failure level set estimation and probability estimation on synthetic
test functions as well as two real-world applications, namely, the reliability
analysis of a gas turbine engine blade using a finite element method and a
transonic aerodynamic wing test case using Reynolds-averaged Navier--Stokes
equations. We demonstrate that our method predicts the failure boundary and
probability more accurately and computationally efficiently while using varying
fidelity models compared with using just a single expensive high-fidelity
model.
