  A computer code can simulate a system's propagation of variation from random
inputs to output measures of quality. Our aim here is to estimate a critical
output tail probability or quantile without a large Monte Carlo experiment.
Instead, we build a statistical surrogate for the input-output relationship
with a modest number of evaluations and then sequentially add further runs,
guided by a criterion to improve the estimate. We compare two criteria in the
literature. Moreover, we investigate two practical questions: how to design the
initial code runs and how to model the input distribution. Hence, we close the
gap between the theory of sequential design and its application.
