Measurement Uncertainty
Why a part passes on one gauge and fails on another
You send a part out. It passes your inspection. It arrives at the customer, they measure it, and it fails. Nobody is lying — both measurements are probably correct within their own uncertainty. The drawing asked a question neither gauge could answer precisely enough to settle the argument.
Measurement uncertainty is not error
Error is being wrong. Uncertainty is the range within which the true value sits. Every measurement has one, including yours.
A caliper reading 49.98 mm does not mean the part is 49.98 mm. It means the part is probably somewhere near 49.98 mm, and how near depends on the instrument, the method, the temperature, and the person holding it.
Where the uncertainty comes from
| Source | What it does |
|---|---|
| Instrument | Resolution and calibration state. A 0.02 mm caliper cannot settle a 0.05 mm tolerance. |
| Temperature | Steel grows about 11.7 µm per metre per °C. |
| Operator | Feel on a caliper, probe force on a CMM, exactly where the reading was taken. |
| Method | Two-point measurement of a bore gives a different answer to a least-squares fit. |
| The part itself | Form error. A hole that is not round has no single diameter. |
The temperature one catches people out
Metrology standards assume 20 °C. A workshop in August is not 20 °C.
A 1000 mm steel part measured at 30 °C reads about 0.12 mm longer than the same part at 20 °C. Aluminium moves roughly twice as far — about 0.23 mm over the same span.
If your tolerance is ±0.1 mm on a metre-long part, temperature alone has eaten the whole budget before anyone touched a gauge.
The rule that keeps arguments short
Your measurement system should consume no more than about 10% of the tolerance you are checking. Some shops accept 4:1. Below that, you are measuring your gauge as much as the part.
Worked through: a ±0.05 mm tolerance has a 0.10 mm band. At 10:1 you need a measurement system good to about 0.01 mm. A workshop caliper is not that instrument, whatever its display says.
What this means for the drawing
Before a number goes on a drawing, three questions are worth asking. What instrument will actually check this? Is that instrument good enough at 10:1? And does the drawing say enough for the inspector to measure it the same way we did?
That third one causes more disputes than the first two combined. A diameter with no indication of how it should be evaluated invites two honest people to measure two different things and disagree.
Why we care
We put tolerances on drawings for a living. A tolerance tighter than the process needs costs money on every part. A tolerance nobody can measure repeatably costs arguments, and eventually a customer.
So we work backwards: what has to be controlled, how will it be checked, and what does the drawing need to say for those two to agree.