3 A posteriori robustness analysis and quality control methodology In this work, we quantify the robustness as the worst case scenario among all possible design configurations due to uncertainty in term of defective or missing spot welds. The structure will be considered more robust which have low worst case variation due to missing of a specific number of spot welds. Alternatively, the structure is to be considered more robust which can afford to loose higher number of spot welds without compromising a specified critical performance limit. As discussed earlier, while a MC simulation is potentially a straightforward way to quantity the robustness of a spot welded structure to defective or missing spot welds, large number of analyses required, renders its use impractical in the present context. Hence, we propose a simple and less costly approach based on an examination of the impact of the most influential spot welds on the performance criteria of interest. It has already been shown that the spot welds with higher indicator values have relatively stronger influence on the eigenfrequencies than the spot welds with lower indicator values [3, 8]. Therefore, they will be used to define a worstcase degradation curve as a function of an increasing number of missing of the most influential spot welds. The goal is to draw the robustness curve showing the sensitivity of performance when the most influential spot welds are defective or missing. This robustness curve allows the impact of the number of defective or missing spot welds on the system performance to be analyzed in order to define a set of critical spot welds that should be quality controlled or reinforced. This curve also serves as a useful tool for deciding how many spot welds should be inspected following assembly while taking into account total number of RSWs and specific robustness level. 3.1 Procedure to obtain the robustness curve The proposed procedure to obtain the robustness curve can briefly be described as follows: 1. all existing spot welds are ranked according to decreasing value of the indicator criteria, 2. a predefined number of spot welds of higher ranks are selected for removal, 3. an analysis is performed to evaluate the impact of removed spot welds on the modal behavior, 4. the indicator criteria is calculated for the remaining spot welds, 5. stop, if stopping criteria is met, otherwise, go to the first step. Q. I. Bhatti and M. Ouisse and S. Cogan 304
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