## 5 Conclusions  
This paper dealt with the enhanced RDO method and its application to the probabilistic strength design problem of seat belt anchorage, as related to the front crash safety of multi-purpose vehicles. In order to quantitatively guarantee the robustness of the constraint, the enhanced RDO method was devised such that not only the robustness of the objective function and the constraint were considered using mean and standard deviation, but also reliability analysis methods, such as MVRM and AISM, were applied to the constraint. Additionally, the probability of reliability was evaluated for the converged optimum results using the MCS to verify the actual reliability. The main research results of this paper are as follows:  
* The strength performances were evaluated by FEA, applying load and boundary conditions to accommodate the actual seat belt anchorage test, which are regulated in ECE and FMVSS. From the result of FEA, it was confirmed that the initial design of the seat frame satisfied the ECE R14 regulation, but the plastic strain margin was more than 50%;
* For the weight minimized design of the seat frame that guarantees structural reliability, the probabilistic design optimization considering the manufacturing uncertainty was carried out. The RDO problem was formulated such that the random design variables were determined by minimizing the seat frame weight subject to the probabilistic strength performance constraints, and were evaluated via reliability analyses as well as the evaluation of the three sigma level robustness, which gave a 99.73% reliability probability on side constraints;
* The probabilistic constraint functions used in the RDO formulation were the maximum plastic strain and dynamic deformation. The thickness sizes were considered the design variables, and the mean value of the design variable was defined as the initial design thickness. Considering that all the seat frame parts were manufactured from a cold-reduced carbon steel sheet, the thickness manufacturing tolerance of the national standard was adopted as the uncertainty for the probabilistic design of the seat frame;
* The RDO results of the seat frame design using the MVRM and the AISM all showed conservative design results as compared to the deterministic optimal design results. The weight reduction results using the RDO with the MVRM and the AISM were 3.4% and 1.7%, respectively, while the weight reduction of the deterministic optimal design was 17.8%;
* In the context of the constraint function results of the plastic strain, the RDO with the MVRM and the AISM ensured a safety margin of more than 50% based on the upper limit value of constraint, while the deterministic optimal design was only 6%, which was approaching the failure limit. Regarding the constraint function results of the dynamic deformation, the RDO with the MVRM and the AISM secured a safety margin of about 20% based on the upper limit value of constraint, while the deterministic optimal design was active on the limit value;
* Reviewing the RDO results according to the reliability analysis method, the RDO results with the AISM were more conservative than the MVRM. It was found that the robustness result on the converged probabilistic optimal design was varied according to the reliability analysis method. The numerical cost was compared based on the number of function evaluations, and the AISM case was the highest because the number of samples increased for the search of the failure region during the reliability analysis;
* From the verification results of MCS, the reliability probabilities for the probabilistic optimal design of the RDO using the MVRM and the AISM all presented results of three sigma or higher.