Recent advances in additive manufacturing enable the precise realization of complex topology-optimized designs. Despite these advantages, additive manufacturing processes, including laser powder bed fusion are prone to process-induced defects, with porosity being one of the most common forms arising from keyholing and lack-of-fusion. Such porosities can adversely affect mechanical performance, particularly by increasing local stresses and reducing fatigue life [1]. Porosity defects emerge from complex interactions among factors such as temperature history, geometric features, and process conditions. While physics-based process models at the microscale can achieve high defect prediction accuracy, their application to part-scale topology optimization remains computationally expensive [2]. This highlight the importance of a balanced modelling strategy in design optimization. This study presents an RBTO framework incorporating stochastic porosity defects in additive manufacturing. For simplicity, this study assumes that the occurrence of defects is linearly dependent on the peak temperature distribution during the part scanning process. We use stress concentration factors based on geometric assumptions to quantify the localized stress amplification induced by porosity defects. This approach reduces the computational cost of RBTO by performing only one FE calculation per iteration and amplifying the stresses using analytical solutions for various pore distributions. The probability of defect occurrence is modelled using binary random variables, avoiding sampling. The proposed RBTO framework aims to obtain optimal designs that minimize volume or compliance while satisfying probabilistic stress constraints. Therefore reliability analysis is conducted using analytical propagation of binary random variables to obtain the mean and standard deviation of the limit state function (P-Norm stress). The results obtained with this method are compared against Monte Carlo simulations . The proposed approach is expected to facilitate the design of reliable components under process-induced defects, contributing to more sustainable additive manufacturing.