Question 19.5: Suppose the statistical tolerance bandwidth for the overall ...
Suppose the statistical tolerance bandwidth for the overall length of the previous example (±0.077 mm) is too large for the particular application. An overall statistical tolerance of ±0.065 mm is required. How can this be achieved?
This can be achieved in several different ways. One way would be to set the tolerance (and hence the standard deviation) equal on all the components:
\sigma_{1}=\sigma_{2}=\sigma_{3}=\sigma_{4}=\sigmaSet \sigma_{z}^{2}=(0.065 / 3)^{2}=4 \sigma^{2}
Hence σ= 0.0108 mm.
Hence the tolerance limits for each individual component would be ± 3σ = ± 0.033 mm. Alternatively, the tolerance limits on, say, components 1 and 4 could be kept the same and the tolerance limits on components 2 and 3 could be tightened.
Suppose we decide that the tolerance limits on items 2 and 3 should be equal (\sigma_{2}=\sigma_{3}).
\sigma_{z}^{2}=\sigma_{1}^{2}+\sigma_{4}^{2}+2 \sigma_{2}^{2}2 \sigma_{2}^{2}=2.69444 \times 10^{-4}
\sigma_{2}=0.0116 mm
So the tolerance limits on components 2 and 3 would need to be ± 0.035 mm in order for the overall tolerance of the assembly to be ± 0.065 mm.