2020/04/03 by Michel Broniatowski, Broniatowski, Michel, Emilie Miranda +1
Decision Sciences · Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #Optimal Experimental Design Methods #Probabilistic and Robust Engineering Design #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.2004.01563
openalex publication_date 2020/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.