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Reliability Based Design Optimization (RBDO) aims to optimize performance function under reliability constraints, which is not considered in the deterministic design optimization. During the past decades, with the advent of powerful computers, lots of literatures focused on developing the methods of RBDO for the accuracy and efficiency. However, with the application of RBDO in various cases, it is always that the reliability target for the whole system is regarded as the reliability target for each probabilistic constraint, and traditional RBDO did not consider system reliability. The RBDO model of crashworthiness for vehicle side impact is the origin where we find the limit of traditional RBDO formulation, which is also a typical model for RBDO. And the of the system reliability compute mode directly influences the formulation of probabilistic constraint function, especially when the number of probabilistic constraint is large-scale. Firstly, the probabilistic approaches for traditional RBDO are introduced, then, the new formulation of RBDO for system reliability is presented, with transforming the traditional RBDO into an expanded RBDO. One numerical example is presented and discussed to demonstrate the difference between expanded RBDO with the traditional RBDO in the mechanical applications.