Aircraft conceptual design traditionally utilizes simplified analysis methods and empirical equations to establish the basic layout of new aircraft. Applying optimization methods to aircraft conceptual design may yield solutions that are found to violate constraints when more sophisticated analysis methods are introduced. The designer's confidence that proposed conceptual designs will meet their performance target is limited when conventional optimization approaches are utilized. Therefore, there is a need for an optimization approach that takes into account the uncertainties that arise when traditional analysis methods are used in aircraft conceptual design optimization. This research introduces a new aircraft conceptual design optimization approach that utilizes the concept of Reliability Based Design Optimization (RBDO). RyeMDO, a framework for multi-objective, multi-disciplinary RBDO was developed for this purpose. The performance and effectiveness of the RBDO-MDO approaches implemented in RyeMDO were evaluated to identify the most promising approaches for aircraft conceptual design optimization. Additionally, an approach for quantifying the errors introduced by approximate analysis methods was developed. The approach leverages available historical data to quantify the uncertainties introduced by approximate analysis methods in two engineering case studies: the conceptual design optimization of an aircraft wing box structure and the conceptual design optimization of a commercial aircraft. The case studies were solved with several of the most promising RBDO-MDO integrated approaches. The proposed approach yields more conservative solutions and estimates the risk associated with each solution, enabling designers to reduce the likelihood that conceptual aircraft designs will fail to meet objectives later in the design process.