QM Bench

Gage R&R Calculator (ANOVA method, AIAG MSA)

Evaluate a crossed Gage R&R study with the ANOVA method. Paste part, operator and repeated measurements on each line to get repeatability, reproducibility, %GRR, % tolerance and ndc.How to use ↓
  1. 1Enter your data
  2. 2Read the verdict
  3. 3Download the PDF report

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Paste your study on the left, import an Excel file, or load the AIAG example.

How to run a Gage R&R study

  1. Select 10 parts that represent the full process range and number them so the operators cannot see the numbers.
  2. Have 3 operators measure every part 2 or 3 times in random order, without seeing their earlier results.
  3. Paste the data as part; operator; trial 1; trial 2; trial 3, one line per part and operator. Long format with one measurement per line also works.
  4. Enter the tolerance (USL − LSL) to also get % of tolerance.

What the results mean

  • Repeatability (EV): variation when the same operator measures the same part repeatedly. High repeatability points to the gauge itself: clamping, resolution, wear.
  • Reproducibility (AV): variation between operators. High reproducibility points to method or training: different technique, reading, fixture use.
  • Part-to-part: the real variation between parts. It should dominate the total.

The verdict follows AIAG MSA 4th edition. The calculator reproduces the AIAG reference example, which you can load with one click.

Formulas (ANOVA method)

The two-way ANOVA splits the total sum of squares into part, operator, interaction and repeatability. The variance components are σ²_repeat = MS_E, σ²_int = (MS_PO − MS_E) / r, σ²_oper = (MS_O − MS_PO) / (p·r) and σ²_part = (MS_P − MS_PO) / (o·r), with negative estimates set to zero. %Study = 100 × σ_component / σ_total, %Tolerance = 100 × 6σ / tolerance.

Once the gauge is approved, use it for a process capability study.

Frequently asked questions

›What is an acceptable %GRR?

According to AIAG MSA, below 10 % of study variation or tolerance is acceptable, 10 to 30 % may be acceptable depending on the application, the cost of the gauge and the risk, and above 30 % the measurement system needs improvement.

›What does ndc mean?

The number of distinct categories is how many groups of parts the gauge can reliably tell apart within the part variation of the study, calculated as 1.41 × part standard deviation / GRR standard deviation. AIAG requires ndc of 5 or more.

›Should I use % of study variation or % of tolerance?

Use % of tolerance when the gauge is used to accept or reject parts against a specification. Use % of study variation when the gauge is used for process control or capability studies. This calculator shows both and bases the verdict on the larger value.

›How many parts, operators and trials do I need?

The classic layout is 10 parts, 3 operators and 2 or 3 trials, so 60 or 90 measurements. Choose parts that cover the real process spread, otherwise the part variation is too small and %GRR looks worse than it is.

›What is the difference between the ANOVA and the range method?

The ANOVA method uses all the information in the data and can separate the operator by part interaction. The range (average and range) method is simpler to calculate by hand. Results are similar but not identical, and ANOVA is preferred by AIAG.

›Why was the interaction term removed?

If the operator by part interaction is not significant (p ≥ 0.25), it is pooled into repeatability, as recommended by AIAG and used by common statistics software. The tool shows which model was used.