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Tolerance stack up5/26/2023 ![]() $$ \large\displaystyle $$Īnd x̄ is the sample mean of the samples. The formula to combine standard deviations of the stack is ![]() The result of adding the means and taking the root sum square of the standard deviations provides an estimate of the normal distribution of the tolerance stack. The variances, not the standard deviations, are additive and provide an estimate of the combined part variation. The bell-shaped curve is symmetrical and fully described with two parameters, the mean, μ, and the standard deviation, σ. RSS assumes the normal distribution describes the variation of dimensions. This, of course, assumes the parts are mostly centered and within the tolerance range. In many cases, the actual individual part dimensions occur near the center of the tolerance range with very few parts with actual dimensions near the tolerance limits. The root sum squared (RSS) method is a statistical tolerance analysis method.
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