The paper proposes an imprecise Fault Tree Analysis in order to characterize systems affected by the lack of reliability data. Differently from other research works, the paper introduces a classification of basic events into two categories, namely Initiators and Enablers. Actually, in real industrial systems some events refer to component failures or process parameter deviations from normal operating conditions (Initiators), whereas others refer to the functioning of safety barriers to be activated on demand (Enablers). As a consequence, the output parameter of interest is not the classical probability of occurrence of the top event, but its Rate of OCcurrence (ROCOF) over a stated period of time. In order to characterize the basic events, interval-valued information supplied by experts are properly aggregated and propagated to the top. To this purpose, the Dempster-Shafer Theory of evidence is proposed as a more appropriate mathematical framework than the classical probabilistic one. The proposed methodology, applied to a real industrial scenario, can be considered a helpful tool to support risk managers working in industrial plants. (C) 2013 Elsevier Ltd. All rights reserved.