Basic events in Probabilistic Safety Assessment (PSA) models are typically quantified independently of the accident sequence and of other failures that lead to a system unavailability. This simplifies quantification of undesirable consequences and in most situations, this approximation does not distort safety indicators. However, there are emerging needs for dependency handling between basic events such as (1) dependencies between operator actions, (2) correlations between events in PSA, e.g., incurred by seismic events, and (3) common cause failure modeling. In these situations, improved handling of dependencies could yield more realistic analysis results and by this increase applicability of safety indicators.
Conditional quantification of basic events presents a flexible, simple, and transparent tool to model these dependencies. At the same time, it poses theoretical and algorithmic challenges to analysis tools. We describe the implementation of the first release of this feature in RiskSpectrum PSA (version 1.5.0, released in 2021), focusing on the choices taken and solutions applied. The aim of this feature is to enable users to specify conditional probabilities of basic events when needed and appropriate, focusing mainly on Human Reliability Analysis (HRA) applications. The solution treats conditional quantification of basic events correctly throughout the whole analysis span, starting with the generation of minimal cut sets (MCS), quantification of the generated MCS list (including the MCS BDD algorithm), merging and post-processing of MCS lists, as well as importance, sensitivity, time-dependency and uncertainty analyses.
Dependency treatment for operator actions removes undeserved bonus when accounting for several human failures within one scenario. Subsequent failures might depend on the fact that the operator has already failed with a previous action. Conditional quantification will then conservatively increase the human error probability, typically according to one of the pre-defined formulas specified in the applied HRA method. The implemented algorithm allows users to specify conditional probabilities as a part of the model and then run a single analysis that efficiently generates all cut sets and correctly applies the cutoff so that no cut set with the value above the cutoff after the conditional quantification is lost. Basic events that obtain a new value from conditional probability are treated as separate events. This resolves possible under-approximations due to the success treatment of conservatively estimated dependent basic events, especially in the MCS BDD quantification of the MCS list. Experiments on industrial-sized models show that our method, compared to the standardly used HRA event replacement in post-processing, can efficiently generate minimal cut sets which would be otherwise missing or discarded.
Further development will focus on extending conditional quantification for other applications. Common cause failure modeling might benefit from a more flexible way to specify dependencies between events. For instance, not fully symmetrical situations might be transparently modeled by specifying conditional probabilities. Correlations between seismic events represent another possible area for conditional quantification, where this concise way of specifying dependencies might improve both modeling and result precision.
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