Measurement uncertainty: why a pass may still be a fail

The pass that is not a pass

A bore measures 10.02 mm against a limit of 10.02 mm and the inspector writes pass. The next inspector, on a different gauge, measures 10.03 mm and writes fail. Both are reading the same part, and both may be right within their own measurement uncertainty. The number on the report is not the part. It is the part plus or minus everything the measurement did to it.

Measurement uncertainty is the range within which the true value is expected to lie, given everything known about the measurement. It is not a mistake and it does not mean the gauge is bad. It is a property of the whole measurement process: the instrument, the fixture, the operator, the temperature, the datum and the method.

What uncertainty is not

Uncertainty is not the resolution of the display. A calliper that reads to 0.01 mm has a resolution of 0.01 mm, but its uncertainty may be several times larger. Resolution sets the smallest change you can see, not how close the reading is to the truth.

It is also not the same as a gauge repeatability and reproducibility study. A gauge R and R study estimates how much variation comes from the gauge and the operators. Those results feed the uncertainty budget, but the budget also includes calibration, temperature, elastic deformation, fixturing and the definition of the characteristic. A good R and R on a badly fixtured part still leaves a large uncertainty.

Where the uncertainty comes from

List the sources before trying to quantify them. The usual ones are repeatability, reproducibility between operators, calibration of the reference, thermal expansion, the stiffness of the part and the fixture, the datum used, and the definition of the feature. For a small pressed part, the clamping force alone can move a reading more than the gauge error.

For a thin or flexible part, the measurement force matters. A micrometer with a ratchet stop and a calliper with a sliding jaw load the part differently, and a flexible leg deflects under one and not the other. For a plated surface, the thickness of the coating becomes part of the dimensional result if the drawing dimension is over plating.

A small budget, worked through

Take an illustrative calliper measurement of a 12 mm dimension on a machined part. Suppose repeated readings on one part give a standard deviation of 0.012 mm. The calibration certificate gives a standard uncertainty of 0.008 mm. The workshop varies by 4 degrees Celsius over the shift, which contributes about 0.006 mm on an aluminium part of this size. Operator differences contribute 0.006 mm, and the fixture and clamping contribute 0.004 mm.

Combine the standard uncertainties in quadrature: the square root of the sum of the squares. With these figures the combined standard uncertainty is about 0.017 mm. Multiply by a coverage factor of 2 for roughly 95 per cent confidence, and the expanded uncertainty is about 0.034 mm. The result should be reported as the reading plus or minus 0.034 mm, with the basis stated.

Those figures are illustrative, but the shape of the answer is not. Repeatability usually dominates, calibration is often second, and temperature and fixturing decide whether the budget is credible. The exercise is worth doing once per measurement family, then reviewing when the gauge, the fixture or the part changes.

Applying a decision rule

A tolerance of 12.00 plus or minus 0.05 mm means the true value must lie between 11.95 and 12.05 mm. If the measurement uncertainty is 0.034 mm, a reading of 12.04 mm cannot prove conformity, because the interval around it crosses the upper limit. A reading of 12.06 mm cannot prove nonconformity for the same reason. The zone between is the uncertainty band, and a decision rule says what to do there.

The simple acceptance rule ignores the band and accepts any reading inside the tolerance. It is common and it quietly passes some nonconforming parts. The guard band rule shrinks the acceptance zone by the uncertainty, so only results that are clearly inside are accepted. A shared risk rule splits the band between the supplier and the customer. ISO 14253-1 sets out the principle that conformity is only proven when the whole interval is inside the tolerance.

When the margin is thin

The wrong response to a thin margin is to argue about the gauge. The right response is to look at the process. If parts sit near the limit and the uncertainty is a significant fraction of the tolerance, the process is not centred or the tolerance is tight for the method. Moving the mean to the middle of the tolerance buys margin without changing the uncertainty at all.

The second response is to reduce the uncertainty where it is cheap. A fixed support instead of hand holding, a temperature soak before measurement, a gauge with better repeatability and a written method can each remove a source. Do not spend on a better instrument if the fixture dominates the budget. The budget tells you where the money goes.

• Centre the process on the nominal, not on the nearest limit.
• Fix the part in the same way every time, with a defined support and force.
• Record the ambient temperature and allow the part to soak.
• Use a gauge whose resolution is well below the uncertainty you need.
• Repeat the budget when the fixture, gauge or part material changes.

Reporting the result

A report that states a measured value and a decision is incomplete without the uncertainty basis. State the expanded uncertainty, the coverage factor and what it covers. Where the customer's drawing or contract defines a decision rule, name it. Where no rule is defined, say which one was applied.

Keep the budget on file with the calibration records. An auditor who sees a conformity decision on a limit will ask how the band was handled. A one page budget, dated and tied to the gauge and the fixture, answers that question in a way that a verbal assurance cannot.