Abstract: In this study, an efficient method is proposed, which we called (TRBDO), to evaluate the probability of failure in closed-form. This method is based on the Function of random variables or transformation together with the finite element method to obtain the Probability Density Function (PDF) using the random variable transformation between the input random variables and the output variable. Once the PDF is evaluated the calculation of the probability of failure Pf is straight forward. To proof the accuracy of the proposed method, the result is compared with Monte Carlo simulation. The efficiency of presented methodology is demonstrated on the design of a 6-bar truss.