Risk Analysis, Vol. 31, No. 1, 2011 DOI: 10.1111/j.1539-6924.2010.01475.x Fault and Event Tree Analyses for Process Systems Risk Analysis: Uncertainty Handling Formulations Refaul Ferdous, 1 Faisal Khan, 1, * Rehan Sadiq, 2 Paul Amyotte, 3 and Brian Veitch 1 Quantitative risk analysis (QRA) is a systematic approach for evaluating likelihood, conse- quences, and risk of adverse events. QRA based on event (ETA) and fault tree analyses (FTA) employs two basic assumptions. The first assumption is related to likelihood values of input events, and the second assumption is regarding interdependence among the events (for ETA) or basic events (for FTA). Traditionally, FTA and ETA both use crisp probabilities; however, to deal with uncertainties, the probability distributions of input event likelihoods are assumed. These probability distributions are often hard to come by and even if avail- able, they are subject to incompleteness (partial ignorance) and imprecision. Furthermore, both FTA and ETA assume that events (or basic events) are independent. In practice, these two assumptions are often unrealistic. This article focuses on handling uncertainty in a QRA framework of a process system. Fuzzy set theory and evidence theory are used to describe the uncertainties in the input event likelihoods. A method based on a dependency coeffi- cient is used to express interdependencies of events (or basic events) in ETA and FTA. To demonstrate the approach, two case studies are discussed. KEY WORDS: Event tree analysis (ETA); fault tree analysis (FTA); interdependence; likelihoods; quantitative risk analysis (QRA); uncertainty SYMBOLS m(p i )/m(c i ) Belief mass m 1−n 1 to n numbers of experts’ knowl- edge n Number of events/basic events Subscript (L) Minimum (left) value of a TFN Subscript (m) Most likely value of a TFN Subscript (U) Maximum (right) value of a TFN 1 Faculty of Engineering and Applied Science, Memorial Univer- sity, St. John’s, NL, Canada. 2 Okanagan School of Engineering, University of British Columbia, Kelowna, BC, Canada. 3 Department of Process Engineering and Applied Science, Dal- housie University, Halifax, NS, Canada. ∗ Address correspondence to Faisal Khan, Faculty of Engineering & Applied Science, Memorial University, St. John’s, NL, Canada A1B 3X5; tel: 709 737 8939; fax: 709 737 4042; fikhan@mun.ca. C d Dependency coefficient N Number of samples P i Probability of events (i = 1, 2, ... , n) ˜ P i Fuzzy probability λ i Frequency ˜ P α TFN with a α-cut P OR “OR” gate operation P AND “AND” gate operation μ Membership function α Membership function at a specific level  Frame of discernment (FOD)  Null set ∩ Symbol for intersection ⊆ Symbol for subsets Bel,Pl Belief, plausibility bpa Basic probability assignment 86 0272-4332/11/0100-0086$22.00/1 C  2010 Society for Risk Analysis