In distributed design systems, while designers are connected to each other through dimensioning couplings, they have limited control over design and performance variables. Any inconsistency among design objectives and working procedures of heterogeneous designers interacting in the design system can result in design conflicts due to these couplings. Modeling design attitudes can help to understand inconsistencies and manage conflicts in design processes. We extend the conventional bottom-up or design supervision approach through agent-based attitude modeling techniques to a more powerful level. In our model, design agents can set requirements directly on their wellbeing values that represent how their design targets are likely to be met at a given moment of the design process. Some design conflicts can in this manner be prevented at an earlier phase of the design process. Set-based design and constraint programming techniques are used to explore the overall performance of stochastic design collaborations on a product modeled with uncertainties at a given moment of the design process. Monte Carlo simulations are performed to evaluate the performance of our set-based thinking approach, providing a variety of agent attitudes. The results show that the number of design conflicts occurring during the design process and the intensity of design conflicts are both reduced through our collaborative design platform.