Modelling uncertainties in limit state functions

• Ordering: pf ≤ p X 6 →Z f ≤ p R,X 6 →Z f and p S f ≤ p RS f ≤ p R,X 6 →Z f . • Strong independence: Complete information about the uncertain limit state function is needed. • Epistemic irrelevance: Sufficient to know q which condenses the uncertain limit state function. q could be a starting point for uncertainty modelling. • Random set independence: Possibility to combine upper probabilities of failure resulting from different and independent computations. • The amount of information to deal with decreases from the uncertain limit state function itself to the function q and to the upper probabilities. Summary (a) If we learn the values of the basic variables x, our knowledge about the parameters z and therefore about the choice of the limit state functions gz does not change. (b) Learning the values of the parameters z and therefore learning which limit state function gz to use has no influence on our knowledge about the variables x. Independence of random variables X and Z