Passive safety systems (PSS) play a central role in advanced nuclear reactor designs, yet their reliability assessment is challenged by strong dependence on complex thermal–hydraulic phenomena and associated uncertainties. This paper presents a response surface based methodology developed under an Electric Power Research Institute (EPRI)–supported study for integrating phenomenological uncertainty into probabilistic reliability analysis of PSS. The approach combines traditional fault tree analysis with uncertainty propagation derived from detailed thermal–hydraulic best estimate simulations. To address the computational impracticality of large scale Monte Carlo sampling with high fidelity codes, response surfaces are constructed from a limited set of best estimate analyses and subsequently used as surrogate models for efficient uncertainty propagation. The methodology is demonstrated through a pilot application to a hypothetical, simplified passive containment cooling system, providing credible insights into system performance and reliability. A third order multivariate polynomial regression is employed to develop the baseline response surface, and alternative parametric and non parametric formulations—including transformed linear regression, Gaussian process regression, and spline based models—are considered to assess their suitability for PSS applications. The paper discusses methodological tradeoffs, data selection strategies, and goodness of fit evaluation metrics, and highlights the implications of response surface choice on reliability estimates. The results support the use of response surface surrogates as a practical and flexible framework for risk informed assessment of passive safety system reliability in advanced nuclear reactors.