In many real world situations, engineers are not able to perfectly model or predict the performance of systems or components due to the quality and amount of information available and the presence of unavoidable uncertainty. Despite the different levels of uncertainty and imprecision, it is still necessary to be able to propagate the uncertainty through the model and quantify the risk. In particular, decision makers need to know the confidence associated with the methodology adopted to model the uncertainty and avoid wrong decisions due to artificial restrictions introduced by the modelling. Hence, a generalized uncertainty quantification tool for dealing with different representation of the uncertainty is needed. This paper presents a generally applicable and efficient strategy to perform extreme case analysis where only limited amount of information is available. This is achieved defining probability boxes, intervals and fuzzy variables to represent the epistemic uncertainty and assessing the reliability computing the failure probability bounds by means of efficient advanced Monte Carlo sampling based on Line Sampling. A novel strategy has been developed to estimate the bounds of the failure probability and to identify the input distributions that best fit the distributions of the extreme realizations.