The Japan Atomic Energy Agency has been developing “Advanced Reactor Knowledge- and AI-aided Design Integration Approach through the whole plant lifecycle (ARKADIA)” to offer the best solutions for challenges in the design and operation of nuclear plants. A part of ARKADIA for design study, which included design optimization of components, is named as ARKADIA-Design. In the development of ARKADIA-Design, we have been developing a process to automatically optimize design parameters of structural components subjected to various kinds of loads, including thermal transients. In this paper, we propose a simplified procedure to estimate the failure probability of components subjected to thermal transients for design optimization. An objective function of this optimization is defined on the basis of failure probability of the components, because failure probability can be commonly used as an indicator of component integrity for various mechanisms, and it helps future introductions of a risk-informed performance-based approach to component design. To enable the necessary number of estimations for design optimization with practical calculation time, we aimed to reduce the number of analyses required for one estimation. For this purpose, we adopted the first-order second-moment (FOSM) method as the estimation method for failure probability in the process of optimization. An orthogonal table in the experiment design method is utilized to define the conditions of the analyses for evaluation of the mean and variance of thermal transient stress, which are used as inputs in the FOSM method. The superposition of ramp responses is also utilized to evaluate the time history of thermal transient stress instead of finite element analysis. The proposed procedure was applied in a demonstration study to optimize the thickness of a cylindrical vessel subjected to thermal transients derived from shutdown. We confirmed that the procedure can evaluate the failure probability depending on the cylinder thickness with practical calculation time.