One of the main uses of Monte Carlo simulation in Six Sigma is with DFSS at the planning stage of a new product. Testing different processes on physical manufacturing or service models or prototypes can be cost prohibitive. Monte Carlo simulation allows engineers to simulate thousands of different outcomes on models without the cost and time associated with physical simulation. Benefits include the ability to experiment with different designs in Design of Experiment models.
The fundamental steps in the Design and Optimize phases of a Design for Six Sigma product development effort involve modeling a physical system using a designed experiment, and using the model to achieve the required system performance using Monte Carlo simulation to estimate system sensitivity and capability. You can see a recorded webcast on this topic given by Bausch & Lomb Worldwide Director of Six Sigma Jeff Slutsky.