Actually, a lot of bibliography points from Limit State Design to FORM (First Order Reliability Method).
Stochastic methods are being widely used into these environments (those of FORM).
But before, lets get a brief review on Limit States:
Limit States Design require the designer to establish a set of performance criteria (vibration levels, deflection, strength, stability, buckling, twisting, collapse,...) for the designed piece.
Then, according to its relevance, the variable of design enters within the area of the safety (ULS) or the comfort (SLS):
- ULS (Ultimate Limit State): Satisfaction of ULS happens when all factored bending, shear, tensile and compressive stresses are below the factored resistances.
- Stresses are magnified
- Resistances are reduced
- SLS (Serviceability Limit State): Satisfaction of SLS happens when deflection, vibration , fissuration,...are within a certain criteria
Here the limits and the factors are prescripted by the regulatory organ, in a probabilistic manner, but are applied in the same deterministic way and within the same deterministic methodology as it has been for decades.