Why measure the measurement
Every number in a capability study, a sorting record or a D6 comparison is measured process spread plus measurement spread. If the gauge spread is large, the Cpk or Ppk you report is too low, good parts get rejected, bad parts get accepted, and a before/after comparison may only show gauge noise.
The parts of the variation
- EV, repeatability: one operator, one gauge, the same part measured several times. Mostly the equipment.
- AV, reproducibility: the difference between operators measuring the same parts. Method, fixture, training.
- GRR: the combination, √(EV² + AV²). Standard deviations add as squares, not directly. A full ANOVA study also reports a part × operator interaction; GRR here is the simplified √(EV² + AV²).
- PV, part variation: the real spread between the parts in the study.
- TV, total variation: √(GRR² + PV²).
Worked example: bore diameter
A bore is specified at 25.00 ± 0.30 mm (tolerance 0.60 mm). A study with 10 parts, 3 operators and 3 trials gives these standard deviations (fictional): EV 0.010 mm, AV 0.006 mm, PV 0.040 mm. Ratios to tolerance use a 6σ spread, as in MSA 4th edition; some software or older studies use 5.15σ, so say which you used.
| Quantity | Calculation | Result |
|---|---|---|
| GRR (σ) | √(0.010² + 0.006²) | 0.0117 mm |
| TV (σ) | √(0.0117² + 0.040²) | 0.0417 mm |
| GRR vs tolerance | 6 × 0.0117 / 0.60 | 11.7 percent |
| GRR vs total variation | 0.0117 / 0.0417 | 28.0 percent |
| ndc | 1.41 × 0.040 / 0.0117 = 4.84, truncated | 4 |
Against the tolerance, this gauge is in the “may be acceptable” band, close to 10. Against total variation it is close to the 30 limit, and ndc 4 is below the usual minimum of 5. So: usable for accept/reject decisions at final inspection if the customer agrees, but weak for SPC or for proving a small process improvement in D6.
Where to look first: EV (0.010) is larger than AV (0.006), which points at the equipment (resolution, clamping, temperature, wear) rather than the operators. Repeatability alone uses 6 × 0.010 / 0.60 = 10 percent of the tolerance.
Common mistakes
- Picking 10 parts from one batch, so PV is tiny and the ratio vs total variation looks terrible (or ndc is 1).
- Operators who know which part they are measuring. Randomise and hide the part number.
- Reporting only the tolerance ratio when the data feeds a capability study.
- Running the study in the lab when the gauge is used at the machine.
- Ignoring resolution: the gauge should read in steps of at most one tenth of the tolerance or of the process variation (common rule).
- No MSA for attribute checks (go/no-go, visual). Use an attribute agreement study instead.
MSA inside an 8D
In D2 and D4, ask whether the escape was a measurement problem: did the gauge see the defect at all? That is often the escape point. In D3, a sorting check is only as good as the check method; write it into the sorting instruction. In D6, show that the gauge used for the before/after data can resolve the difference you claim (see D6 verification).
FAQ
- What is a good Gage R&R result?
- A widely used rule of thumb (AIAG MSA manual): GRR under 10 percent is generally acceptable, 10 to 30 percent may be acceptable depending on the application, cost and risk, and over 30 percent needs improvement. Your customer's requirements decide which basis (tolerance or total variation) and which limit apply.
- Should I compare GRR to the tolerance or to the total variation?
- Tolerance tells you whether the gauge can judge good vs bad parts. Total variation (or process variation) tells you whether it can see the process move, which is what SPC and capability studies need. State which one you report; they can give very different answers.
- What is ndc?
- The number of distinct categories: roughly how many groups of parts the gauge can tell apart within the process spread, computed as 1.41 × PV / GRR and truncated to a whole number. A common minimum is 5.
- How many parts, operators and trials?
- A common crossed study is 10 parts, 3 operators, 2 or 3 trials each. The parts should cover the real process range, not 10 consecutive parts from one setting.
- Do I need an MSA in an 8D?
- If D4 or D6 relies on measurements of the failed characteristic, yes: a poor gauge can hide the defect, create false rejects, or make a fix look effective when it is not.