Title: Probabilistic risk bounds for the characterization of radiological contamination,
Abstract: The radiological characterization of contaminated elements (walls, grounds,
objects) from nuclear facilities often suffers from a too small number of
measurements. In order to determine risk prediction bounds on the level of
contamination, some classic statistical methods may then reveal unsuited as
they rely upon strong assumptions (e.g. that the underlying distribution is
Gaussian) which cannot be checked. Considering that a set of measurements or
their average value arise from a Gaussian distribution can sometimes lead to
erroneous conclusion, possibly underconservative. This paper presents several
alternative statistical approaches which are based on much weaker hypotheses
than Gaussianity. They result from general probabilistic inequalities and
order-statistics based formula. Given a data sample, these inequalities make it
possible to derive prediction intervals for a random variable, which can be
directly interpreted as probabilistic risk bounds. For the sake of validation,
they are first applied to synthetic data samples generated from several known
theoretical distributions. In a second time, the proposed methods are applied
to two data sets obtained from real radiological contamination measurements.