Modelling uncertainties in limit state functions

In this paper uncertainties in limit state functions g as arising in engineering problems are modelled by adding additional parameters and by introducing parameterized probability density functions which describe the uncertainties of these new additional parameters and of the basic variables of g. This will lead to a function pf(a, b) for the probability of failure depending on parameters a and b corresponding to the two parameterized density functions. Further the parameters a and b   are assumed to be uncertain. Using intervals, sets or random sets to model their uncertainty results in upper probabilities p¯f of failure. In this context we also discuss different notions of independence such as strong independence, epistemic irrelevance and random set independence and present a simple engineering example.

► In this paper uncertainties in limit state functions g as arising in engineering problems are modelled by adding additional parameters and by introducing parameterized probability density functions which describe the uncertainties of these new additional parameters and of the basic variables of g. ► We develop a function pf(a, b) for the probability of failure depending on parameters a and b   corresponding to the two parameterized density functions. ► Using intervals, sets or random sets to model their uncertainty results in upper probabilities p¯f of failure. ► We also discuss different notions of independence such as strong independence, epistemic irrelevance and random set independence and present a simple engineering example.