Rock property uncertainties are broadly categorized into aleatory (due to inherent variability) and epistemic (due to limited or subjective data). This paper presents a mixed-reliability model to address these uncertainties, modeling properties with limited input data as convex variables and sufficiently available data as random variables in rock tunnel stability analysis. The method utilizes a super-ellipsoid-based convex model for limited input data uncertainties and stochastic methods for random variables. The convex model-based non-probabilistic reliability index ( \(\beta^{C} )\) is defined as the minimum distance from the origin to the failure surface. A hybrid algorithm, combining Monte Carlo simulations and convex model-based reliability measure, is developed to estimate the pdf of \(\beta^{C}\) . Illustrated with a rock tunnel case study, this approach accurately accounts for input uncertainties for evaluating reliability measure by propagating mixed input uncertainty based on exact information, rather than assumed probability distributions. It advances traditional methods by accounting for input uncertainties without subjective assumption, offering a more informed understanding of tunnel stability.