Formalizing Quantitative Risk Analysis: Probabilistic Foundations and Monte Carlo Methods - Jönsson,Johan (Bachelor’s Theses in Mathematical Sciences, 2025)
Quantitative Risk Analysis (QRA) for hazardous materials facilities remains dominated by event tree partitioning into discrete scenarios, with many calculations performed manually. This study formalizes the classical individual and societal risk metrics within the framework of probability theory. The resulting framework enables deeper theoretical inquiry and makes underlying assumptions explicit. This framework also enables quantitative risk analyses to utilize more advanced Monte Carlo methods commonly employed in more mature risk management disciplines. A full year case study is presented for a hypothetical ammonia installation in Malmö, Sweden. The simulation combines ERA5 2024 meteorological data with a time-varying Gaussian puff model and a stochastic two-phase leak-rate generator. A total of 8 784 hourly realizations are compared against a conventional 216-scenario QRA that follows recommendations for a typical quantitative risk analysis. The Monte Carlo approach reproduces directional variability without the angular averaging required by the scenario method and eliminates the need for 100% lethality assumptions within a fixed radii. The study demonstrates that a fully probabilistic QRA enhances clarity in the interpretation of risk measures and yields more precise spatial risk estimates with minimal additional analyst effort. Because the framework is grounded in probability theory, it imposes no strict constraints on model selection. These attributes position Monte Carlo QRA as a viable alternative to coarse scenario sets in future safety assessments.
Keywords: Quantitative risk analysis; Quantitative Risk Assessment; QRA; Probability theory; Individual risk; Societal risk; Monte Carlo simulation; Stochastic Processes