Probabilistic dynamics: A comparison between continuous event trees and a discrete event tree model

The feeling that dynamics and their interaction with the random evolution of parameters was ill-treated in classical probabilistic safety assessment methodologies led to the development of probabilistic dynamics methodologies. These methods explicitly model the mutual influence between physical variables, operators and components, using different basic assumptions. This paper is a first attempt at a systematic comparison between two such methodologies, namely, DYLAM and the continuous event tree (CET) theory on a simple problem. The problem involves one bistate component and one physical variable whose evolution depends on the component current state and that should not, in any case, cross a prespecified threshold. The methods are briefly discussed. In particular, we show how DYLAM can be derived as a special case of the CET theory. The numerical implementation of each method is also reviewed. Each method is then applied to the specific problem. The probability of system failure over time is compared to its real, analytically derived, value. We focus on key issues such as exactness, stability and efficiency. We point out the main differences between the methods and draw a first set of conclusions as to their respective fields of application, recognizing, however, that the analysis should be carried further on more complex problems to reach definitive conclusions.