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We propose a sequential design method aiming at the estimation of an extremequantile based on a sample of dichotomic data corresponding to peaks over agiven threshold. This study is motivated by an industrial challenge in materialreliability and consists in estimating a failure quantile from trials whoseoutcomes are reduced to indicators of whether the specimen have failed at thetested stress levels. The solution proposed is a sequential design making useof a splitting approach, decomposing the target probability level into aproduct of probabilities of conditional events of higher order. The methodconsists in gradually targeting the tail of the distribution and sampling undertruncated distributions. The model is GEV or Weibull, and sequential estimationof its parameters involves an improved maximum likelihood procedure for binarydata, due to the large uncertainty associated with such a restrictedinformation.

A sequential design for extreme quantiles estimation under binary sampling