  As models in various fields are becoming more complex, associated
computational demands have been increasing significantly. Reliability analysis
for these systems when failure probabilities are small is significantly
challenging, requiring a large number of costly simulations. To address this
challenge, this paper introduces Reliability analysis through Error rate-based
Adaptive Kriging (REAK). An extension of the Central Limit Theorem based on
Lindeberg condition is adopted here to derive the distribution of the number of
design samples with wrong sign estimate and subsequently determine the maximum
error rate for failure probability estimates. This error rate enables optimal
establishment of effective sampling regions at each stage of an adaptive scheme
for strategic generation of design samples. Moreover, it facilitates setting a
target accuracy for failure probability estimation, which is used as stopping
criterion for reliability analysis. These capabilities together can
significantly reduce the number of calls to sophisticated, computationally
demanding models. The application of REAK for four examples with varying extent
of nonlinearity and dimension is presented. Results indicate that REAK is able
to reduce the computational demand by as high as 50% compared to
state-of-the-art methods of Adaptive Kriging with Monte Carlo Simulation
(AK-MCS) and Improved Sequential Kriging Reliability Analysis (ISKRA).
