Try it while you read
Open the free Type 1 Gauge Study (Cg, Cgk) tool and click Load sample: it reproduces the case study below.
Theory: repeatability and bias on one part
The Type 1 study is the first check of a new or repaired gauge. One master part with a known reference value is measured many times by one operator. Because the part and the operator do not change, all variation comes from the gauge itself. Two things are evaluated: the spread of the readings and the bias, the difference between their mean and the reference value.
T is the tolerance (USL − LSL), s the standard deviation of the repeated readings and K the share of the tolerance the gauge may use, usually 20 %. Cg answers “is the spread small enough?”, Cgk adds “and is the gauge centred on the truth?”. Both should be at least 1.33.
Bias test
A t-test checks whether the bias is statistically different from zero: t = bias / (s / √n). A significant bias is not automatically a failure; it matters only if it eats a large part of the allowed band, which Cgk already captures.
Resolution
The gauge resolution should be at most 5 % of the tolerance (the 10:1 rule is the older version of this idea). A coarse resolution makes the readings jump between a few values and the standard deviation becomes unreliable.
Key point
Step by step
- Pick the master: a calibrated part or setting master with a reference value close to the middle of the tolerance.
- Measure 50 times (at least 25). Remove and re-clamp the part every time, as in production.
- Enter the values in the tool’s column, then the reference value, the tolerance and the resolution.
- Read Cg and Cgk against 1.33 and look at the run chart for trends (warming up, drift).
- Check the bias and the resolution percentage.
Case study: gauge for a 10.000 mm diameter
A digital gauge with 0.0001 mm resolution will check a diameter of 10.000 mm with a tolerance of 0.100 mm. A master of exactly 10.0000 mm is measured 50 times. (This is Load sample in the tool.)
| Statistic | Value |
|---|---|
| Mean | 10.00098 mm |
| Standard deviation s | 0.001155 mm |
| Bias | +0.00098 mm (t = 5.99, p < 0.001) |
| Cg | 2.89 |
| Cgk | 2.60 |
| Resolution | 0.10 % of tolerance |
Both indices are far above 1.33: the gauge is capable. The bias of about 1 µm is statistically significant because the gauge repeats so well, but it uses only a small part of the allowed band. The team still corrects the zero point during the next calibration and continues with a Gage R&R.
Common mistakes
- Measuring without re-clamping: the spread looks better than in real use.
- Using a production part instead of a calibrated master: the bias cannot be evaluated.
- Too few readings (10 or 15): s is too uncertain.
- Ignoring a trend in the run chart, which usually means temperature effects.
Frequently asked questions
Why 20 % of the tolerance?
The usual convention (Bosch booklet 10, VDA 5) allows the measurement spread to use 20 % of the tolerance, so K = 20. Some companies use 15 % or 10 % for critical characteristics. The tool lets you change K.
Cg is fine but Cgk is not, what does that mean?
The gauge repeats well but reads systematically off. Check the master value, the calibration and the zero setting; often a simple offset correction solves it.
Is the Type 1 study in the AIAG MSA manual?
Not under that name. It comes from the German automotive practice (Bosch, VDA 5) and is widely required by German OEMs. The AIAG equivalent ideas are the bias and repeatability studies.