Abstract: Two new methods, diagrammatical approximation and Monte Carlo Iteration, are introduced to search for design point and acquire reliability index. The two methods are developed based on geometrical principles. Several formulas are presented to calculate random variables of distributed type in accordance with standard normal variables. Improvements are made to simplify the computation process and enhance the efficiency of solution. If the two methods are combined, the solution efficiency will be even higher. Numerical examples are provided to demonstrate the feasibility of the methods. It is shown that satisfactory accuracy of solution can be achieved.