Quantifying the Conditional Dependencies between Layers of Protections in Event Tree Analysis

An approach to include conditional probabilities when calculating probabilities of disaster in quantitative risk analysis is presented.¹ Since not all layers of protection are independent of each other, using conditional probabilities leads to more accurate calculations of probabilities of disaster in a chemical process. Based on event tree analysis, probabilities of disaster are calculated assuming that events are statistically independent (independence assumption), and separately considering that events affect each other (conditional probabilities), in three cases with increasing complexity and number of layers of protection. First, a simple alarm – operator case is studied, then two cases involving a chemical reactor and operator with increasing number of layers of protection are analyzed. For all cases, we considered multiple scenarios to show that results do not depend on the input probabilities of particular events. For the latter two cases, the input probabilities of each event were randomly sampled with Monte Carlo simulations. Probabilities of disaster calculated with the assumption of statistical independence were compared to probabilities of disaster calculated with conditional probabilities. In most scenarios of the three cases, findings show that the probabilities of disaster calculated using the independence assumption are lower than those with conditional probabilities, which can lead to undercounting the layers of protection that are needed. Process engineers need to be aware that assuming that events are statistically independent can lead to the possibility of undercounting of layers of protection needed for a chemical process.

Reference: Mott TC, Kivistik PM, Panorska AK, Cantu DC. Comparing conditional probabilities and statistical independence in layers of protection analysis. Proc Safety Prog. 2020;e12215. https://doi.org/10.1002/prs.12215