Despite the critical importance of project completion timeliness, management practices in place today remain inadequate for addressing the persistent problem of project completion tardiness. Uncertainty has been identified as a contributing factor in late projects. This uncertainty resides in activity duration estimates, unplanned upsetting events, and the potential unavailability of critical resources. This research developed a comprehensive simulation based methodology for conducting quantitative project completion-time risk assessments. The methodology enables project stakeholders to visualize uncertainty or risk, i.e. the likelihood of their project completing late and the magnitude of the lateness, by providing them with a completion time distribution function of their projects. Discrete event simulation is used to determine a project's completion distribution function. The project simulation is populated with both deterministic and stochastic elements. Deterministic inputs include planned activities and resource requirements. Stochastic inputs include activity duration growth distributions, probabilities for unplanned upsetting events, and other dynamic constraints upon project activities. Stochastic inputs are based upon past data from similar projects. The time for an entity to complete the simulation network, subject to both the deterministic and stochastic factors, represents the time to complete the project. Multiple replications of the simulation are run to create the completion distribution function. The methodology was demonstrated to be effective for the on-going project to assemble the International Space Station. Approximately $500 million per month is being spent on this project, which is scheduled to complete by 2010. Project stakeholders participated in determining and managing completion distribution functions. The first result was improved project completion risk awareness. Secondly, mitigation options were analyzed to improve project completion performance and reduce total project cost.