Selecting a calculation method

By John Raffaldi and Steven Ramsier, Ph.D.

Typically, GR&R studies require two or three appraisers, and between five and 10 trials to establish the EV and AV measurement error components. However, if an automated test system lacks appraiser variation, the instantaneous GR&R calculation method that uses the within-subgroup standard deviation calculations can be used. The instantaneous method uses only one appraiser and provides information only on the within-system, EV component. If fewer than 10 measurements are taken, correction factors must be considered. These factors listed in the table, c4 Values, are taken from Acheson Johnston Duncan's book, "Quality Control and Industrial Statistics." Otherwise, use a value of c4 = 1 as the correction factor for more than 10 measurements. For the instantaneous method, the calculations are as follows:

1. Calculate the standard deviation from the trials. If using multiple parts and multiple trials, calculate the standard deviation for each set of individual part measurements, and then take the average of the standard deviations just calculated. The result is the average standard deviation.

2. Divide the standard deviation by the correction factor, c4, if using fewer than 10 trials. The number of observations in the sample, n, is the number of trials. This information is shown in the table, c4 Values.

3. Multiply the number from step 2 by the number of sigma to be used, usually 5.15 or 6.

4. Divide the number from step 3 by the tolerance, which is the upper specification limit (USL) minus lower specification limit (LSL), and multiply by 100 to obtain the GR&R as a percentage of the tolerance.

The formula is: % GR&R = ((5.15 * ó / c4) / (USL - LSL))*100 or % GR&R = ((6 * ó / c4) / (USL - LSL))*100 where sigma equals the standard deviation for the trials or one part or the average standard deviation from multiple part or trial measurements.