  We propose a sequential design method aiming at the estimation of an extreme
quantile based on a sample of dichotomic data corresponding to peaks over a
given threshold. This study is motivated by an industrial challenge in material
reliability and consists in estimating a failure quantile from trials whose
outcomes are reduced to indicators of whether the specimen have failed at the
tested stress levels. The solution proposed is a sequential design making use
of a splitting approach, decomposing the target probability level into a
product of probabilities of conditional events of higher order. The method
consists in gradually targeting the tail of the distribution and sampling under
truncated distributions. The model is GEV or Weibull, and sequential estimation
of its parameters involves an improved maximum likelihood procedure for binary
data, due to the large uncertainty associated with such a restricted
information.
