Shared autonomous electric vehicles (SAEVs) are a promising car-sharing service expected to be implemented in the near future. However, existing studies on the optimization of SAEV systems do not consider uncertainties in the SAEV systems, which may interfere with the achievement of the desired performance or objective. From the perspective of the company, a SAEV system should be designed to minimize the total cost while securing the targeted wait time of the customer, but uncertainties in the SAEV system can cause variation in the customer wait time, which can lead to inconveniences to customers and damage to the reputation of the company. Therefore, this study considers the uncertainties in a SAEV system and applies reliability-based design optimization (RBDO) to the design of the SAEV system to minimize the total cost of system design while satisfying the target reliability of the customer wait time. A comparison of the optimization results of various wait time constraints and probabilities of failure provides observations on applying RBDO to the design of a SAEV system. Furthermore, several insights can be obtained through various parametric studies. From this study, it is verified that RBDO can be successfully applied to the design of a SAEV system and a design framework for the SAEV system that can both lower the cost and ensure the reliability of the customer wait time is proposed.