This question is about manufacturing tolerances; for instance, a manufactured component expressed as "$5 \pm 0.3\,\mathrm{in}$" may acceptably be no larger than 5.3 in and no smaller than 4.7 in.
I know how to perform mathematical operations on uncertainties; since uncertanties are expressed statistically, adding two uncertain values involves adding the root of the sum of the squares of the uncertanties. Details here.
However, tolerances aren't statistical; they express the intent of the designer. In addition, tolerances may be asymmetrical. Let's say I have two dimensions with tolerances:
$$ X = 50\pm3\,\mathrm{mm} \\ Y = 30^{+3}_{-0}\,\mathrm{mm}$$
How would I calculate the tolerances for $(X+Y)$ and $(X-Y)$?
Illustration for $(X+Y)$:
Assume that $X$ and $Y$ are the critical dimensions for the intended use, but the machinist needs to start with $(X+Y)$ to cut the initial block of material.