Uncertainty quantification in bow-tie analysis: A mixed approach of fuzzy theory with Dempster-Shafer theory of evidence

Bow-Tie analysis is a very prominent method to analyze risks related to the occurrence of undesirable events in critical industrial facilities. It provides a detailed investigation on an unwanted event starting from its causes to its undesired consequences, with the consideration of the risk controls presented to mitigate the probability of occurrence (POC) of these events. Bow-tie analysis also presents an effective quantitative technique in calculating the probabilities of risks. However, the credibility of quantitative analysis using Bow-Tie is still a major concern because of uncertainty. The unavailability of statistical and precise input data often restrict the performance of the analysis. In this case, expert knowledge represents an alternative in providing an elicitation on the unavailable data. This elicitation may be attached with uncertainty related to imprecision, ignorance and the lack of consensus if multiple experts opinions are used. Fuzzy theory and Dempster Shafer theory (DST) of evidence are the most powerful techniques to deal with these sources of uncertainty. This paper proposes a methodology to (i) characterize uncertainty in the probability of input data, (ii) combine multiple uncertain knowledge from multiple sources of data and (iii) propagate these characterizations and combinations through the Bow-Tie model in order to characterize uncertainty in the output. This methodology is based on a mixture of fuzzy numbers with the DST of evidence for richer handling of imprecision, ignorance and the lack of consensus in risk analysis. Finally to describe the utility of this methodology, its application on a case study of the most common accident in a chemical facility has been derived.