Building an Error Budget for Inline Diameter Measurement

An error budget is the sum of everything that can move a measurement away from the true value, written out term by term so you can see which term dominates. It is the document that stops a project from buying an instrument with a ±2 µm figure and then discovering the installation delivers ±15 µm. This page builds one for a transmitted-light inline diameter gauge, using the published POMEAS LM-1030 figures as the instrument term, and shows how to add the terms that vendors do not publish.

Step 1: Separate the Two Instrument Numbers

The LM-1030 datasheet gives ±2 µm measurement accuracy and ±0.15 µm repeatability. These are not interchangeable and mixing them is the single most common error in a procurement spec:

• Repeatability (±0.15 µm) is the spread of repeated readings on the same object under the same conditions. It tells you whether the instrument is stable, not whether it is right.
• Accuracy (±2 µm) is agreement with true size. It is the term you compare against a tolerance.

If your control plan gates on whether a part is in tolerance, accuracy is the governing figure. Repeatability matters for detecting small changes over time — tool wear, for instance — where you are looking at deltas rather than absolute size. Budget both, and know which one each requirement depends on.

Step 2: Add the Terms Nobody Publishes

The instrument is one line in the budget. The rest come from the installation:

Step 3: Combine Them Honestly

Budget terms that are independent and random are combined as the square root of the sum of squares, not by straight addition — straight addition assumes every term is simultaneously at its worst, which is pessimistic. But if a term is systematic rather than random — thermal growth of the fixture is a good example, because it pushes readings one way — it adds directly and does not get the root-sum-square discount. The discipline is to classify each term before combining them, then state the result as a band with its conditions rather than as a single number.

Step 4: Check the Budget Against the Tolerance

The rule of thumb used in gauge capability is that the measurement system should consume a small fraction of the tolerance band — commonly expressed through gauge repeatability and reproducibility studies rather than a fixed ratio. The practical point: if your tolerance is ±5 µm and your budget totals ±4 µm, the gauge cannot reliably separate good parts from bad ones regardless of how good the instrument is on its own. At that point the options are to widen the tolerance if the design allows, to improve presentation, or to change the measurement principle — the trade-offs of moving the measurement off the line altogether are set out in choosing a flash measurement machine.

Worked Example

A wire line runs at a speed that, at 35 µs exposure, contributes negligible blur. The product is 8 mm stock with a ±10 µm diameter tolerance. Instrument accuracy ±2 µm. Pass-line wander held within the depth of field contributes an estimated ±1 µm. Vibration estimated at ±1 µm. Thermal drift over a shift estimated at ±2 µm, systematic. Window contamination budgeted at ±1 µm. Combining the random terms by root-sum-square gives about ±2.4 µm; adding the systematic thermal term directly brings the band to roughly ±4.4 µm against a ±10 µm tolerance. That is a workable budget. Repeat the same exercise with a ±3 µm tolerance and the answer is no.

Where the Numbers Come From, and Their Limits

The ±2 µm and ±0.15 µm figures are the LM-1030 specification-table values. Note that the LM-1030 brochure headline quotes ±0.06 µm repeatability while the specification table quotes ±0.15 µm; the test conditions for the headline figure are not published, and this site uses the specification-table value. Every other term in the budget above is estimated for the example and must be measured on your own installation — they are not instrument specifications and should not be copied into a procurement document as if they were. Verification method and interval are covered in calibration and measurement stability.

FAQ

Should I write the tolerance against accuracy or repeatability?

Accuracy, if you are deciding whether a part is in tolerance. Repeatability governs whether you can see small changes over time. The LM-1030 publishes ±2 µm accuracy and ±0.15 µm repeatability; they answer different questions.

How do I combine the error terms?

Independent random terms combine as the square root of the sum of their squares. Systematic terms — those that push readings consistently one way, such as thermal growth of a fixture — add directly. Classify each term before combining.

Why is my real measurement worse than the datasheet?

Because the datasheet describes the instrument, and your reading includes pass-line wander, vibration, thermal growth, contamination, product condition and calibration drift. Those terms usually dominate. Build the budget and measure them rather than assuming.

Can telecentric optics remove pass-line error entirely?

They remove the size change that comes from axial movement — within the specified depth of field. Outside that depth, or with lateral wander beyond the measurement window, position still matters. Fixturing is still required.

What fraction of the tolerance should the measurement system consume?

Small enough that the gauge can separate conforming from non-conforming parts with confidence. This is normally settled with a gauge repeatability and reproducibility study rather than a fixed percentage; the practical test is whether your budget total leaves clear margin against the tolerance band.

Does the error budget change for transparent product?

Yes, and materially. Transmitted-light gauging depends on a clean shadow; translucent or clear stock does not produce one reliably. See inline measurement of transparent and reflective parts.

Next Step

Send the tolerance, the product diameter, the line speed and the material, and we can help you put real numbers against each term — including whether a transmitted-light gauge such as the LM-1030 is the right principle at all. For principle selection, start with inline diameter measurement methods.