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 measurement device.

• For determining the Repeatability of the measurement system, we'll look at the differences between the measurement trials of the same parts.

• The Repeatability statistic is s_E (or EV.) The sub-E in s_E stands for (Measuring) Equipment; EV stands for Equipment Variation.

• 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.

• Reproducibility is the difference in measurements between appraisers.

• The Reproducibility statistic is s_A (or AV).

  • The sub-A in s_A stands for Appraisers.
  • AV stands for Appraiser Variation.

where:

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.