Reliability methods are used to deal with the variability in rock properties. These methods require probabilistic characteristics of properties, to be estimated via large quantities of objective data. This data is difficult to obtain due to different difficulties in rock testing, and/or subjective nature of certain properties. This invokes epistemic uncertainties in properties as indicated by their information levels, impeding the application of probabilistic reliability methods. This study proposes a non-probabilistic reliability methodology for problems with insufficient information of inputs. The methodology is further generalized to mixed uncertainty problems. A super-ellipsoid convex model with minimized volume is used to model objective inputs with limited data. The subjective inputs are modelled as fuzzy/interval models. The super-ellipsoid model is mapped to a unit multi-dimensional sphere, with non-probabilistic reliability index (βNP) defined as the shortest distance from its origin to the limit surface. A double-loop optimization algorithm is developed to estimate fuzzy/intervals of βNP. The method is demonstrated for a rock slope, with inputs modelled via mixed uncertainty models. The method efficiently estimates the converged fuzzy/intervals of βNP by propagating the impreciseness of inputs. The effect of variations in uncertainty and convex models of inputs on βNP is further investigated.