fault tree analysis (fta) as a probabilistic risk assessment (pra) method is used to identify basic causes leading to an undesired event, to represent logical relation of these basic causes in leading to the event, and finally to calculate the probability of occurrence of this event. to conduct a quantitative fta, one needs a fault tree along with failure data of the basic events (bes). someti...

We study continuous (strongly) minimal cut generating functions for the model where all variables are integer. We consider both the original Gomory-Johnson setting, as well as a recent extension by Cornuéjols and Yıldız. We show that for any continuous minimal or strongly minimal cut generating function, there exists an extreme cut generating function that approximates the (strongly) minimal fu...

a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

Consider a network of pipes joining a set of intakes (the source) to a separate set of outlets (the e n sink), so that liquid flows from the intakes, through the network, to the outlets. A cross-section of th etwork, separating the intakes on one side from the outlets on the other, is called a cut. A minimal t c cut is one that, roughly speaking, slices through a set of pipes whose combined cap...

Constructing new, complex models is often done by reusing parts of existing models, typically by applying a sequence of segmentation, alignment and composition operations. Segmentation, either manual or automatic, is rarely adequate for this task, since it is applied to each model independently, leaving it to the user to trim the shapes and determine where to connect them. In this paper we prop...

The reliability of a two-terminal flow network with a discrete set of possible capacities for its arcs is usually computed in terms of minimal path or minimal cut vectors. This paper analyzes the connection between minimal path vectors and flow functions, which supports the development of an efficient algorithm that solves the problem of finding the set of all such vectors.