Question

Consider an assembly characteristic X = X1 + X2 - X3. The specification (tolerance) limits on X are 3.00 ± 0.05 in. Let the characteristics X1, X2, and X3 be normally and independently distributed with means m1 = 0.5 in., m2 = 1.50 in., and m3 = 1.00 in., respectively. The variances of the characteristics are equal. The processes are selected such that 99.73% of the characteristics fall within the tolerance limits. The means of the characteristics are equal to the respective basic sizes. It is desired that 99.9937% of the assembly characteristic falls within the tolerance limits 3.00 ± 0.05 in. Determine the tolerances (Ti , i = 1, 2, and 3) on the characteristics X1, X2, and X3 using the probabilistic tolerance relationship.

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