The assessment of a structure’s resistance and performance is directly linked with reliability and safety issues, as

well as with intervention decisions and their relative cost. This assessment can be enhanced by the use of

probabilistic models, invoked by the random nature of load and resistance effects. Moreover, intrinsic properties of

such models should relate to the commonly encountered dependencies among the input random variables. With

respect to that, a significant advance towards effective modelling in current practice of structural reliability

engineering has been achieved by integrating scalar indices, such as correlation coefficients. However, case may be

that this approach overlooks, or even induces considerable uncertainties. Therefore, models which acknowledge and

estimate this uncertainty type can serve the requirements for high reliability and robust decision–making. In the

present study, the uncertainties pertaining to multivariate idiosyncrasy are discussed, and a generalised dependence

structure paradigm is suggested in order to explicitly handle such uncertainties. The predictive potential of resulting

models is demonstrated on an application on fracture mechanics, while the influence on contemporary assessment

procedures is discussed. The corresponding numerical techniques can facilitate the inclusion of advanced correlation

modes in the simulation methods of structural performance.