R & R Repeatability and
Reproducibility
R&R, GR&R, or gauge R & R is a
concept to insure stabile measurements where a single person gets the
exact same results each and every time they measure and/or collect data
measurements. This can be necessary to ensure data consistency and
stability. There are different ways to perform this. The following is an
abbreviated explanation using the method recommended by the AIAG,
(Automotive Industry Action Group). It is used in most quality plans
including six sigma and ISO9000.
This will give you an approximation of the variation
and percent of process variation for the total
measurement system and its component's repeatability, reproducibility and
part to part variations. The formulas to do this analysis and the proper
sequence to follow is below.
Repeatability
EV = Equipment Variation
r = 4.56 for 2 trials, 3.05 for 3 trials
Reproducibility
AV = Appraiser Variation
k = 3.65 for 2 appraisers, 2.7 for 3 appraisers
Repeatability and
Reproducibility
Part Variation
PV = Part Variation
Rp = Range of part averages
j= Depends on number of parts
| Part |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| j |
3.65 |
2.7 |
2.3 |
2.08 |
1.93 |
1.82 |
1.74 |
1.67 |
1.62 |
Total Variation
TV = Total Variation
Percentage of total variation is calculated
using the formulas below
| %EV = 100(EV/TV) |
| %AV = 100(AV/TV) |
| %R&R = 100(R&R/TV) |
| %PV = 100(PV/TV) |
Guidelines for acceptable results are...
| < 10% |
Satisfactory |
| 10%-30% |
May be satisfactory.
Depends on the magnitude of the use, cost of new gauges, cost of
repairs, etc. |
| > 30% |
Unsatisfactory. Take
corrective action. |
For additional information see Quantifying
uncertainties from a gauge study
|
