ABSTRACT
X and the parameter b provides parameters for each value of x for the shape of fb x
Example: Let b(x) = (μ(x), σ) and
f y f y eb Y Y
) )= = −
σ π 1 2
the density of a Gaussian distribution with mean values μ(x) = g(x) at each x and constant variance σ2 replacing the function values of an ordinary limit state function g depending on one variable x. The variable x is assumed to be Gaussian distributed too with parameters μ' and σ ' and density
A realisation of such a probability of failure
pf (a, b) = pf ((μ', σ'), (g, σ))
may look like Figure 1. By means of the function pf (a, b) we have an
interface for controlling the behavior of the probability distributions used for modelling the uncertainty of the basic variables x and the uncertainty of the output of the limit state function. In a further step the two parameters a and b are assumed to be uncertain too using intervals, sets or random sets which results in an upper probability pf of failure.
