how do we treat tolerances in mathematical operations?

Question

A pipe with outer diameter A = 9.2 ± 0.1 , inner diameter B = 7.2 ± 0.1
The thickness of the pipe wall would be C = A – B = 2 ± ??
What is the tolerance for value C

In general, how do we treat tolerances in mathematical operations?

Answer 1

In general, the meaning of "+/-" is that it defines the "one sigma" width of the "bell" curve of the "normal" statistical distribution. Forgive the "", these are specific terms from mathematics. If the two tolerances are "normally" distributed (assume that is so in this case), then the square root of the sum of their squares is the answer to your question. So, it is 0.1414....

Answer 2

The usual way of handling tolerances is simply adding their magnitude. The PROPER way of handling tolerances is √Σ. In you example the tolerance of the answer s/b ± √0.02, or ± 0.141. this is because tolerances are based on standard deviation (quite often ± 3σ) and σ is an rms value. What you are really doing here is adding distributions:
P(9.1 ≤ A ≤ 9.3) = 0.97
P(7.1 ≤ B ≤ 7.3) = 0.97
so
P(1.86 ≤ A - B ≤ 2.14) = 0.97