The three study numbers are ranges, and ranges have to be converted into estimates of spread before they can be compared. The conversion uses multiplying constants that depend on the number of trials, appraisers, and parts; those constants come from a reference table that accompanies any Gage R&R worksheet, and you look them up rather than memorize them. After conversion you have four spread values, each in the same units as the gage.
Equipment variation, EV, is the repeatability spread converted from R-bar. Appraiser variation, AV, is the reproducibility spread converted from the appraiser difference, with a small correction that removes the repeatability already inside it. Part variation, PV, is converted from Rp. These spreads combine by squaring, adding, and taking the square root, because independent sources of variation add that way. Square root means the number that multiplied by itself gives the total.
GRR = square root of (EV² + AV²). Total variation, TV = square root of (GRR² + PV²). The decision figure is %GRR = GRR ÷ TV × 100. Many plants also report %GRR against tolerance = GRR ÷ tolerance width × 100, which answers whether the gage can tell good parts from bad ones. Report both; they answer different questions.
Standard Procedure
- 1Convert R-bar, appraiser difference, and Rp to EV, AV, and PV using the constants from the worksheet's reference table.
- 2Compute GRR = square root of (EV² + AV²).
- 3Compute TV = square root of (GRR² + PV²).
- 4Compute %GRR = GRR ÷ TV × 100 and %GRR of tolerance = GRR ÷ tolerance width × 100.
Lesson Summary
- ✓Spreads combine by squares, so GRR is always less than EV + AV added directly.
- ✓Report %GRR against both total variation and tolerance; they answer different questions.