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A Sequential Design for Extreme Quantile Estimation Under Binary Sampling.

Michel Broniatowski1, Emilie Miranda1

  • 1Laboratoire de Probabilités, Statistique et Modélisation (LPSM), CNRS UMR 8001, Sorbonne Universite, 75005 Paris, France.

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Summary
This summary is machine-generated.

This study introduces a sequential design for estimating extreme quantiles from binary failure data. The method progressively explores distribution tails using conditional probabilities for improved material reliability analysis.

Keywords:
binary informationextreme quantile estimationextreme value theorysequential designsplitting

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Area of Science:

  • Statistics
  • Reliability Engineering
  • Materials Science

Background:

  • Estimating extreme quantiles is crucial for material reliability.
  • Binary data from failure trials presents estimation challenges due to limited information.
  • Existing methods may struggle with the uncertainty inherent in such data.

Purpose of the Study:

  • To propose a novel sequential design method for estimating extreme quantiles from binary data.
  • To address the industrial challenge of material reliability by estimating failure quantiles.
  • To develop a robust procedure for analyzing limited, binary outcome data.

Main Methods:

  • A splitting strategy decomposes extreme probabilities into conditional probabilities.
  • Sampling under truncated laws facilitates exploration of distribution tails.
  • An enhanced maximum likelihood procedure is adapted for binary data.
  • GEV (Generalized Extreme Value) and Weibull models are considered for the underlying distribution.

Main Results:

  • The sequential design enables progressive estimation of extreme quantiles.
  • The method effectively handles binary data and associated uncertainties.
  • Parameter estimation for GEV and Weibull models is improved.

Conclusions:

  • The proposed sequential design offers a robust approach for extreme quantile estimation with binary data.
  • This method enhances material reliability assessments in industrial settings.
  • The enhanced maximum likelihood procedure provides a viable solution for limited information scenarios.