Reliability sensitivity analysis is concerned with measuring the influence of
a system's uncertain input parameters on its probability of failure.
Statistically dependent inputs present a challenge in both computing and
interpreting these sensitivity indices; such dependencies require discerning
between variable interactions produced by the probabilistic model describing
the system inputs and the computational model describing the system itself. To
accomplish such a separation of effects in the context of reliability
sensitivity analysis we extend on an idea originally proposed by Mara and
Tarantola (2012) for model outputs unrelated to rare events. We compute the
independent (influence via computational model) and full (influence via both
computational and probabilistic model) contributions of all inputs to the
variance of the indicator function of the rare event. We compute this full set
of variance-based sensitivity indices of the rare event indicator using a
single set of failure samples. This is possible by considering d different
hierarchically structured isoprobabilistic transformations of this set of
failure samples from the original d-dimensional space of dependent inputs to
standard-normal space. The approach facilitates computing the full set of
variance-based reliability sensitivity indices with a single set of failure
samples obtained as the byproduct of a single run of a sample-based rare event
estimation method. That is, no additional evaluations of the computational
model are required. We demonstrate the approach on a test function and two
engineering problems