The article presents an approach to evaluation the reliability index of steel truss bars with the uncertainty of random variables expressed in the presence of information only about the bounds of variability. Different methods of estimating the bounds of variability for random variables are presented. The new approach is also developed using the provisions of the theory of possibility and the Dvoretzky–Kiefer–Wolfowitz inequality (DKW). The reliability index allows to compare various design solutions by the safety criterion, identify structural elements with the highest failure probability for monitoring the technical state and to quantify the increase in the safety level with strengthening of structural elements. The Monte Carlo statistical simulation data reflect the analogy of the non-probabilistic reliability index in the considered approach with the non-failure probability of the truss bar.