Quantitative risk analysis (QRA) is a fundamental part of the decision-making process when it comes to the safety of people and the environment. However, due to the uncertainty involved, the credibility of risk assessment results is still a major issue. This paper aims to explore the most commonly used approaches to quantify uncertainty in risk analysis: interval analysis, fuzzy theory, probability theory, evidence theory, and the mixed probabilistic-fuzzy approach. These approaches are used to characterize uncertainty in model inputs obtained from different sources, such as statistical data and expert judgments, and to which different types of uncertainty can be attached. These uncertainty characterizations are then propagated through the model to obtain the corresponding representation of uncertainty for the model outputs. The paper presents the application of these quantification approaches to a loss of containment scenario (LOC), representing one of the most likely situations to occur in industry. The overall aim is to study the effects of uncertainty and compare the different approaches. Indeed, the uncertainty quantification approaches presented can lead to different representations of uncertainty in the outputs and hence to different decisions. The use of an inappropriate approach in an inappropriate place may lead to under or overestimation of risk and subsequently to a bad decision. (C) 2017 Elsevier Ltd. All rights reserved.