A computational method for taking into account backward uncertainty propagation in flow problems is presented and applied to the study of rarefaction shock waves (RSW) in a dense-gas shock tube. Previous theoretical and numerical studies have shown that a RSW is relatively weak and that the prediction of its occurrence and intensity are highly sensitive to uncertainties on the initial flow conditions and on the fluid thermodynamic model. The objective of this work is to introduce an innovative, flexible and efficient algorithm combining computational fluid dynamics (CFD), uncertainty quantification (UQ) tools and metamodel-based optimization in order to obtain a reliable estimate for the RSW probability of occurrence and to prescribe the experimental accuracy requirements ensuring the reproducibility of the mea- surements with sufficient confidence.