**1. Introduction**

Accidents at industrial facilities may result in serious consequences to workers, public, property, and the environment. Risk management approaches are aimed at insuring that processes and systems are designed and operated to meet "acceptable or tolerable risk levels" as required by regulatory bodies. Risk assessment usually encompasses the following steps: hazard identification, risk analysis, and risk evaluation. When the risk evaluation is carried out in a quantitative way, the risk assessment is considered a probabilistic risk assessment (PRA).

Fault tree analysis (FTA) and event tree analysis (ETA) are the most used techniques in PRAs. However, uncertainties in PRAs may lead to inaccurate risk level estimations and consequently to wrong decisions [1]. Lack of knowledge about systems under study during the PRAs is one of the main causes of uncertainties, which leads to simplification of assumptions, as well as imprecision and

inaccuracies in the parameters used as inputs to PRA (e.g., component reliabilities, failure probabilities, and human error rates).

A framework to use the method of moments for determining the likelihoods of different outcomes from event trees in an uncertain data environment using fault trees is described in this work. Illustrative examples using this approach for propagating uncertainty in basic events of fault trees, following log-normal distributions, are also presented. The probability distributions of top events are compared with analyses available in the literature using different approaches, such as Monte Carlo simulation and Wilks and Fenton-Wilkinson methods.
