What Is Nested GR&R and When Should You Use It for Destructive Testing?

If you measure a product and then scrap it, you cannot measure the same part twice. That creates a problem for a standard Gage R&R study, which assumes every operator measures the same parts. The solution is Nested GR&R — the approach recommended by the AIAG MSA manual for destructive measurement systems.

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What It Is

Nested GR&R (Gage Repeatability and Reproducibility) is a measurement system analysis method used when the measurement process is destructive — the part is altered or destroyed during measurement, so it cannot be re-measured by another operator or in another trial.

Because the same part cannot be measured repeatedly, the study is designed so that each operator measures a unique set of parts. The parts are assumed to come from a homogeneous batch, and the variation between those parts is treated as "part-to-part" variation within each operator's sample.

The key difference from a standard crossed GR&R: in a crossed study, every operator measures the same parts; in a nested study, each operator measures different parts that are considered equivalent.

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How It Works: Steps and Formula Logic

The analysis follows a nested ANOVA structure, as described in the AIAG MSA manual (Section on Destructive Testing / Nested Designs).

Typical study design:

• Select a number of operators (e.g., 3).
• Select a number of parts per operator (e.g., 10), drawn from the same production batch.
• Each operator measures each of their parts once (or twice, if the test allows two readings before destruction — but usually once).

ANOVA model (nested):

\[
Y_{ijk} = \mu + O_i + P_{(i)j} + E_{ijk}
\]

Where:

• \(Y_{ijk}\) = measurement value
• \(\mu\) = overall mean
• \(O_i\) = operator effect (random)
• \(P_{(i)j}\) = part effect nested within operator (random)
• \(E_{ijk}\) = repeatability error (random)

Variance components estimated:

• \(\sigma^2_{operator}\) — operator-to-operator variation
• \(\sigma^2_{part(operator)}\) — part-to-part variation within each operator's sample
• \(\sigma^2_{repeatability}\) — measurement error (repeatability)

Key calculations:

• Repeatability (EV) = \(\sqrt{\sigma^2_{repeatability}}\)
• Reproducibility (AV) = \(\sqrt{\sigma^2_{operator}}\)
• GRR = \(\sqrt{EV^2 + AV^2}\)
• %GRR = (GRR / Total Variation) × 100, where Total Variation includes part variation.

Acceptance criteria (AIAG):

• %GRR < 10% — acceptable
• 10% ≤ %GRR ≤ 30% — conditionally acceptable
• %GRR > 30% — unacceptable, needs improvement

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A Worked Illustrative Example

Example data (illustrative only):

Three operators, each measuring 5 unique parts from the same batch, one measurement per part.

Operator | Part | Measurement (units)

• A | 1 | 10.2
• A | 2 | 10.5
• A | 3 | 10.1
• A | 4 | 10.4
• A | 5 | 10.3
• B | 6 | 10.6
• B | 7 | 10.4
• B | 8 | 10.7
• B | 9 | 10.5
• B | 10 | 10.6
• C | 11 | 10.0
• C | 12 | 10.2
• C | 13 | 10.1
• C | 14 | 10.3
• C | 15 | 10.2

Using nested ANOVA (computed via statistical software), suppose the variance components are:

• \(\sigma^2_{operator} = 0.04\)
• \(\sigma^2_{repeatability} = 0.01\)
• Part variation (within operators) = 0.03

Then:

• EV = \(\sqrt{0.01} = 0.10\)
• AV = \(\sqrt{0.04} = 0.20\)
• GRR = \(\sqrt{0.10^2 + 0.20^2} = \sqrt{0.05} \approx 0.224\)

If total variation (including part-to-part) is 0.50, then:

\[
\%GRR = \frac{0.224}{0.50} \times 100 = 44.8\%
\]

Interpretation: The measurement system is not acceptable (>30%). The dominant source is operator variation (AV), suggesting operator training or clearer measurement procedures are needed.

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Common Pitfalls

1. Assuming parts are homogeneous — If the batch is not uniform, part variation within operators inflates the GRR estimate. Use a well-mixed, single batch.
2. Using a crossed design by mistake — If operators measure the same part twice (impossible for destructive tests), the analysis is invalid.
3. Too few parts per operator — AIAG recommends at least 5–10 parts per operator; fewer reduces statistical confidence.
4. Ignoring the "one reading per part" limitation — If the test allows two readings before destruction, you can treat them as repeated measurements, but only if the second reading is truly independent.

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Get Started with a Free Tool

Running a nested GR&R by hand is tedious and error-prone. Use the free, structured calculator at https://www.6sq.com/tools/nested_grr/ to enter your operator-part data and obtain variance components, %GRR, and a clear pass/fail verdict — following the AIAG MSA method for destructive testing.