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SummaryOwing to the severe technological competition and high demand for safety estimation in complex physic and engineering systems, reliability analysis has drawn more and more attention. The regular non‐probabilistic reliability analysis assumes that experimental data are enclosed by ellipse and rectangle; however, this appears inconsistent with various types of uncertain sources. In this article, a novel definition for non‐probabilistic reliability is provided for structures based on super parameteric convex model, which is formulated as the ratio of the multidimensional volume located in the safety domain to that of the total super parametric volume. Subsequently, a sampling method is proposed based on Monte Carlo simulation as a reference algorithm. To improve the efficiency, a first‐order calculation method is developed to solve the reliability model using a linear approximation of the limit state function. Furthermore, a second‐order calculation method is constructed to improve the reliability calculation precision with high nonlinearity, and a new non‐probabilistic reliability‐based design optimization method is established accordingly. Six numerical examples are tested to demonstrate the effectiveness of the proposed method.