R&R Analysis for Non-Destructive Measurements
An example of a GR&R application appropriate for non-destructive
measurements is checking part dimensions with a micrometer.
- For example, 2 appraisers could each measure 5 parts, 2 times.
First, look at the Repeatability.
Repeatability looks at the variation between measurements of the
same part when measured by the same appraiser with the same
For determining the Repeatability of the measurement system, we'll
look at the differences between the measurement trials of the same
The Repeatability statistic is sE (or EV.) The sub-E in sE
stands for (Measuring) Equipment; EV stands for Equipment
- We use 5.15 because 5.15 standard deviations is an estimation
of 99% of the variation. AIAG (Automotive Industry Action Group)
allows the option to set Repeatability for 6s to cover 99.7% of the
measurement equipment variation.
Next, look at the Reproducibility.
DIFF = (highest of appraiser grand averages) - (lowest of appraiser
grand averages); actually a range value
dA = d2 value for Reproducibility
n = number of parts
r = number of trials, or runs
The R&R will tell us the total variation in the measurement system
that comes from Repeatability and Reproducibility together.
- To calculate R&R, add the squares of both the standard deviation
values for Repeatability and the Reproducibility and then take the
square root of the result.
To determine if the R&R variation is acceptable or unacceptable...
- Compare the Measurement System Variation to the total variation and
to the tolerance.
- To compare the R&R to the total variation:
- To compare the R&R to the total tolerance:
Is the %GR&R acceptable or not?
If %GR&R represents >30% of the total process variation or takes
up >30% of the total tolerance, the measurement system must be
improved or replaced.
If %GR&R <30% but >10%, the measurement system is marginal.
If %GR&R <10%, the measurement system is acceptable.