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In performing stochastic simulations using computer models, the method of sampling is important. It affects the quality and the convergence speed of the results. This paper discusses one special case: sampling of spot-weld locations from potentially thousands of spot welds on a vehicle body. This study is prompted by the need of evaluating the effect of missed spot welds on the structural integrity, identifying critical welds, and optimizing weld locations. A balanced random sampling algorithm based on the concept of Latin-Hypercube sampling is developed for this application. We also present a case study in which the efficiency of three different sampling methods is compared using a car joint stiffness example. The new method, called the Balanced Latin-Hypercube Sampling (BLHS), has shown significantly faster convergence over the other two.