In this paper, we propose non-parametric estimations of robustness and reliability measures approximation error, employed in the context of constrained multi-objective optimisation under uncertainty. These approximations with tunable accuracy permit to capture the Pareto front in a parsimonious way, and can be exploited within an adaptive refinement strategy. First, we illustrate an efficient approach for obtaining joint representations of the robustness and reliability measures, allowing sharper discrimination of Pareto-optimal designs. A specific surrogate model of these objectives and constraints is then proposed to accelerate the optimisation process. Secondly, we propose an adaptive refinement strategy, using these tunable accuracy approximations to drive the computational effort towards the computation of the optimal area. To this extent, an adapted Pareto dominance rule and Pareto optimal probability computation are formulated. The performance of the proposed strategy is assessed on several analytical test-cases against classical approaches. We also illustrate the method on an engineering application, performing shape optimisation under uncertainty of an Organic Rankine Cycle turbine.