This project develops a statistical framework for understanding Digital Twins, a next-generation technology that integrates modeling, data collection, prediction, and decision-making in a two-way, real-time cycle for a physical, biological, or engineering system. This project explores a Digital Twin for a robotic surgical plate bending system that is integrated into a virtual surgical planning process to assist surgeons in planning and executing cranio-facial reconstructive surgery. This Digital Twin could maintain synchronized models of a human mandible after traumatic injury and a surgical fixation plate designed to stabilize it. A robotic plate bender - part of the system’s physical asset - would iteratively bend the plate, monitor changes in its shape, update the corresponding digital model, and plan the next bending operation, all in real time. This model is then coupled with the patient’s jaw geometry to ensure that the applied forces will not induce long-term weakening or failure. Each step of this complex process involves uncertainty, including errors in the plate or mandible models, noisy observations, and unmodeled variation in the robot’s performance. These uncertainties propagate throughout the Digital Twin system in nonlinear, interacting ways, posing potential risks to patient outcomes. Current Digital Twin frameworks often ignore or oversimplify these sources of uncertainty. This project addresses the critical need for robust, real-time methods to quantify, pro