Robust Event Tree Analysis — Uncertainty-Aware Risk Propagation

Standard ETA assigns a single point probability to each branch and multiplies them along paths to get scenario frequencies. Robust ETA replaces point estimates with probability distributions or intervals, propagates these through the tree (typically via Monte Carlo simulation), and reports scenario frequencies as distributions rather than single numbers. The structural tree logic is identical; the difference is in how uncertainty in the inputs is represented and carried through the calculation.

The most common representations are probability distributions (log-normal or beta distributions are typical for failure probabilities), confidence intervals derived from classical frequentist estimation, Bayesian posterior distributions (especially when expert elicitation is combined with historical data), and imprecise probabilities or probability boxes (p-boxes) when even the distribution family is uncertain. The choice depends on the available data and the regulatory or technical standard being applied.

When any of the following conditions hold: key branch probabilities are based on fewer than ~30 historical observations, expert opinions on a probability span more than half an order of magnitude, the risk conclusion (e.g., acceptable vs. unacceptable frequency) would change if input probabilities moved within their plausible range, or regulators specifically require uncertainty characterization in the safety case. For mature, data-rich systems with small parameter uncertainty, standard ETA is usually sufficient.

Yes, and it often is. In a full probabilistic risk assessment, fault trees are used to compute the probability of each barrier failing (the branch probabilities in the event tree), and those fault tree results carry their own uncertainty. Robust ETA then takes the uncertain barrier failure probabilities as inputs and propagates them forward through the consequence tree. This integrated approach — sometimes called a fully coupled robust PRA — provides end-to-end uncertainty quantification from component failure rates to top-level accident scenario frequencies.

Dedicated PRA tools such as SAPHIRE (developed for the U.S. Nuclear Regulatory Commission), RiskSpectrum, and OpenPSA support ETA with uncertainty quantification. General platforms such as MATLAB, Python (with SciPy, PyMC, or the pbox library), and R can implement Monte Carlo-based robust ETA from scratch. For imprecise probability methods, specialized libraries implementing Dempster-Shafer theory or p-box arithmetic are available in Python and MATLAB.