Building performance calculations often use deterministic simulations. Since many influencing parameters are generally inherently uncertain, this may lead to unreliable predictions of design impact and hence excessive deviations between design and reality. Such excessive deviations of building performances are usually undesirable: clients want guarantees that their investments have the desired impact. Hence, the overall aims of this research are (1) the development of a probabilistic robust design methodology to incorporate these uncertainties for building performance analysis and optimisation and (2) its illustrative application on the thermal design of comfortable and affordable robust low-energy dwellings. In the developed methodology, several design options can be compared based on the probability distributions of the studied performances. In order to do so, a multi-layered Monte Carlo uncertainty analysis is performed to subject all options to the same input uncertainties and hence calculate the corresponding performance distributions. An additional sensitivity analysis is applied to investigate which input uncertainties are most dominant for these distributions. Because this approach might be very time-consuming, the computational model is in this thesis optionally replaced by a much faster meta-model, without compromising the reliability. The methodology also enables an explicit evaluation of the design options for potential scenarios, such as the user type or economic evolutions, when desired. In order to numerically compare the probability distributions in view of the robust design principles, effectiveness and robustness indicators are introduced. Here, effectiveness is defined as the ability of the design option to optimise the performance, while robustness is defined as the ability to stabilise this performance for the entire range of input uncertainties.At the end of the thesis, the methodology is illustrated on the thermal design of comfortable and affordable robust low-energy dwellings. Although this application is simplified, general observations can be made. Most attention needs to be paid on the ventilation system and air tightness, since ventilation losses are more important than conductive heat losses when U-values around 0.2 W/m2K are applied for walls, roofs and floors. In order to avoid overheating in summer, sunscreens seem to be essential. Furthermore, raising awareness for the impact of user behaviour, night ventilation and the size of the dwelling seem to be as important as the application of energy efficient measures.