Gage R&R K1, K2, K3 Constants Table (Average and Range Method)
The average and range gage R&R method uses three constants, K1, K2 and K3, to turn ranges into standard deviation-based estimates. This table lists the values for the common study layouts so you can check a spreadsheet, a QMS export or a hand calculation.
| Constant | Depends on | Count | Value | Used for |
|---|---|---|---|---|
K1 | Number of trials | 2 | 4.56 | EV = Rbar-bar x K1 (repeatability) |
K1 | Number of trials | 3 | 3.05 | EV = Rbar-bar x K1 (repeatability) |
K2 | Number of operators | 2 | 3.65 | AV uses X-diff x K2 (reproducibility) |
K2 | Number of operators | 3 | 2.7 | AV uses X-diff x K2 (reproducibility) |
K3 | Number of parts | 2 | 3.65 | PV = Rp x K3 (part variation) |
K3 | Number of parts | 3 | 2.7 | PV = Rp x K3 (part variation) |
K3 | Number of parts | 4 | 2.3 | PV = Rp x K3 (part variation) |
K3 | Number of parts | 5 | 2.08 | PV = Rp x K3 (part variation) |
K3 | Number of parts | 6 | 1.93 | PV = Rp x K3 (part variation) |
K3 | Number of parts | 7 | 1.82 | PV = Rp x K3 (part variation) |
K3 | Number of parts | 8 | 1.74 | PV = Rp x K3 (part variation) |
K3 | Number of parts | 9 | 1.67 | PV = Rp x K3 (part variation) |
K3 | Number of parts | 10 | 1.62 | PV = Rp x K3 (part variation) |
Values are the 5.15-sigma (99 percent) constants for the average and range method as published in the AIAG MSA reference manual, so EV, AV, GRR and PV come out as 5.15-sigma spreads. A 6-sigma convention exists with different constants. Do not mix constants from different spreads in one study.
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Where each constant is used
K1 converts the average range across all operator and part cells into equipment variation, EV = Rbar-bar x K1. K2 converts the range of operator averages into appraiser variation: AV = sqrt((X-diff x K2)^2 - EV^2 / (n x r)), where n is parts and r is trials. K3 converts the range of part averages into part variation, PV = Rp x K3. Then GRR = sqrt(EV^2 + AV^2) and TV = sqrt(GRR^2 + PV^2).
- K1 depends only on the number of trials
- K2 depends only on the number of operators
- K3 depends only on the number of parts
Worked example
Take 3 operators, 10 parts and 2 trials. With Rbar-bar of 0.0021 mm, EV = 0.0021 x 4.56 = 0.0096 mm. If the operator averages differ by 0.0014 mm, X-diff x K2 = 0.0014 x 2.70 = 0.0038 mm, and AV = sqrt(0.0038^2 - 0.0096^2 / 20), which is about 0.0000 after the subtraction goes slightly negative, so AV is set to zero. Negative values under the square root should always be treated as zero.
Common mistakes
People often apply the 10-part K3 to a study that used 5 parts, or the 2-trial K1 to a three-trial study. Check the layout first. Another frequent slip is mixing a 6-sigma convention with these 5.15-sigma constants, which makes %GRR look different from what an auditor recomputes. The average and range method also cannot separate the operator by part interaction, so use ANOVA when interaction matters.
When to use ANOVA instead
ANOVA is more informative than average and range because it estimates the operator by part interaction and handles unbalanced data. It does need software. The average and range method remains common because it can be done on a worksheet and is accepted by most customers. Whichever you pick, state the method on the report.
Frequently Asked Questions
Why is K2 for 2 operators 3.65?
The constants are the reciprocal of d2* values for the sample size involved, scaled to a 5.15-sigma (99 percent) spread. With 2 operators the range of operator averages is based on a sample of size 2, giving 3.65. With 3 operators the value drops to 2.70.
Can I use these with a 6-sigma study?
No. The 6-sigma convention has its own constants, so using these values would give inconsistent answers. Pick one spread, state it on the report, and use only its matching constants.
What if I have more than 3 operators?
The standard table covers 2 or 3 operators. For larger studies, use ANOVA or compute the constant from d2* tables for the corresponding sample size, and document the method in the study report.
Do I need at least 10 parts?
The classic layout is 10 parts, 3 operators and 2 or 3 trials. Fewer parts reduce the precision of the part variation estimate. Choose parts that span the real process range, not just parts that happen to be on the bench.
If you compute gage R&R by hand in several plants, we can help standardise the calculation and store results against the gage in your ERP.
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