Probability and convexity concepts are not antagonistic

This study is devoted to two objectives to illustrate that the probability and convexity concepts are not antagonistic and to introduce a new non-probabilistic convex model for structural reliability analysis. It is shown that the new measure of safety is easier to evaluate than the corresponding measure utilizing the interval analysis. Moreover, interrelation between the classical probabilistic method and convex modeling method is demonstrated. The purpose of this study is not to replace the probabilistic approach by the convex modeling method, but to illustrate that the probability and convexity concepts are compatible. Some numerical examples are presented to illustrate the feasibility of the proposed methodology.