Some Measure Theoretic Issues in Probabilistic Dynamics

Probabilistic dynamics (or continuous event tree approach) is a methodology used for the probabilistic risk assessment of systems where statistical dependence between failure events may arise because of indirect coupling through the controlled/monitored physical process and/or direct coupling through software/hardware/human intervention. Both the continuous and discrete time/space forms of the probabilistic dynamics frameworks assume that the set of possible trajectories describing the evolution of the system as a function of time in its state-space consists of measurable (and hence compact) subsets. Using a reduced-order boiling water reactor model, it is shown that this assumption may not be valid for systems of practical interest to nuclear engineering. The consequences of violating the measurability assumption on the probabilistic model accuracy are illustrated for the discrete time/state-space approach. Some guidelines for the choice of time/state discretization are also proposed.