ABSTRACT
Two key issues are traditionally encountered at this stage: (a) how to deal with the highly-limited sampling information directly available on uncertain input variables in real-world industrial cases; (b) how to account for quite different natures of uncertainties, such as the traditionally-distinguished intrinsic aleatory uncertainties and reducible epistemic uncertainties. Indeed, a long debate (Apostolakis 1990, Helton 1993, Pathe-Cornell 1996, Helton & Oberkampf 2004) originating from the first large risk assessments in the US nuclear domain has ended up with the importance of distinguishing two types of uncertainty : namely the epistemic (or reducible, lack of knowledge, by ignorance) type referring to uncertainty that decreases with the injection of more data, modeling or number of runs and the aleatory (or irreducible, intrinsic, variability, by essence) type for which there is a variation of the true characteristics that may not be reduced by the increase of data or knowledge.
