Title: The Geometry of Limit State Function Graphs and Subset Simulation,
Abstract: In the last fifteen the subset sampling method has often been used in
reliability problems as a tool for calculating small probabilities. This method
is extrapolating from an initial Monte Carlo estimate for the probability
content of a failure domain found by a suitable higher level of the original
limit state function. Then iteratively conditional probabilities are estimated
for failures domains decreasing to the original failure domain.
But there are assumptions not immediately obvious about the structure of the
failure domains which must be fulfilled that the method works properly. Here
examples are studied that show that at least in some cases if these premises
are not fulfilled, inaccurate results may be obtained. For the further
development of the subset sampling method it is certainly desirable to find
approaches where it is possible to check that these implicit assumptions are
not violated. Also it would be probably important to develop further
improvements of the concept to get rid of these limitations.