Process plants may be subjected to dangerous events. Different methodologies are nowadays employed to identify failure events, that can lead to severe accidents, and to assess the relative probability of occurrence. As for rare events reliability data are generally poor, leading to a partial or incomplete knowledge of the process, the classical probabilistic approach can not be successfully used. Such an uncertainty, called epistemic uncertainty, can be treated by means of different methodologies, alternative to the probabilistic one. In this work, the Evidence Theory or Dempster-Shafer theory (DST) is proposed to deal with this kind of uncertainty. In particular, the classical Fault Tree Analysis (FTA) is considered when input data are supplied by experts in an interval form. The practical problem of information acquisition from experts is discussed and two realistic scenarios are proposed. A methodology to propagate such an uncertainty through the fault tree up to the Top Event (TE) and to determine the belief measures is supplied. The analysis is illustrated by means of two simple series/parallel systems. An application to a real industrial safety system is finally performed and discussed. (C) 2012 Elsevier Ltd. All rights reserved.