In conclusion, an analyst can use this approach to select the design taking into account trade-offs between the total number of spot welds, the impact of missing spot welds, and the number of quality controlled spot welds to ensure a specific level of satisfaction. 20 40 60 80 100 120 140 160 180 −4 −3 −2 −1 0 1 α − Number of RSWs Afford to Loose Relative Eigenfrequency Shift (%) 0 RSWs 10 RSWs 20 RSWs 30 RSWs 40 RSWs Fig. 10 Effect of increased number of quality controlled RSWs 4 Conclusions An optimization procedure is presented which iteratively adds and removes spot welds to find the optimal distribution as well as the number of spot welds needed to improve the performance characteristics of interest. Meanwhile, the structural performances can be undermined by the presence of defective or missing spot welds due to manufacturing defects or fatigue. A simple approach is formulated to analyze the impact of the number of defective or missing spot welds on the system performance with the goal of replacing the more cost intensive sampling based approaches found in the literature. This approach can not only provide a measure of robustness but also could serve as a useful tool to provide insight into the most influential spot welds as well as for deciding how many spot welds should be inspected following assembly. The analyst can then ensure a specific level of robustness either by quality controlling or redesigning of these small number of spot welds. Q. I. Bhatti and M. Ouisse and S. Cogan 308
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