When assembling optical systems, uncertainties of the positioning system and overall mounting tolerances lead to the deterioration of performance due to resulting misaligned optical components. In this paper, we present a novel methodology for the correction-less assembly of optical systems based on predictive tolerance bands. By running a simulation model in parallel to the assembly process, performance predictions can be made during the assembly that take into account the uncertainties of the positioning system. Typically, optical performance can be assessed by a variety of criteria. In this paper, we utilize the Marechal criterion based on the root mean square (RMS) error as it allows to verify if the optical system is defraction-limited. The extension with Monte Carlo methods enables the prediction of mean values and standard deviations for the chosen metric. This is done for the entire optical system yet to be assembled by integrating uncertainties of the positioning system within the simulation framework. Before assembly, a desired threshold (here the RMS value derived from the Marechal criterion) can be specified which is predicted and monitored throughout the assembly process. For verification, we analyze a two-lens system in simulation to demonstrate our proposed framework.