A bottom-up procedure to calculate the Top Event probability in presence of epistemic uncertainty

Industrial plants may be subjected to very dangerous events. Different methodologies are employed to evaluate the probability of their occurrence, as Process Safety Analysis (PSA) or Risk Analysis (RA). However, since for rare events reliability data are poor, the epistemic uncertainty needs to be considered. In this context, the classical probabilistic approach cannot be successfully used and then different approaches must be taken into account. Actually, this paper proposes the use of the Evidence Theory or Dempster-Shafer Theory (DST) to deal with data characterizing rare events in high risk industrial sites. In particular, a classical Fault Tree Analysis (FTA) is considered when the only available information on input reliability data is constituted by expert judgments. Actually, since it is reasonable assuming that experts are unlikely able in supplying point estimates, basic events will be defined by means of real intervals in which they estimate the probability of occurrence could belong to. Preliminarily, the problem of acquiring such information is discussed and two realistic scenarios are proposed. Then, in order to characterize each basic event with a single interval, expert judgments are aggregated according to the DS aggregation rules. Finally, a methodology to propagate such uncertainty through the Fault Tree up to the Top Event and to determine the cumulated belief measures is proposed. An application to a real safety system operating in a refinery plant is shown.