How to Perform an Instantaneous Gage R&R

Measure at least 10 parts. Have the operator measure the parts at least three times. Present the parts in a random order to the operator so he does not know he is measuring the same part repeatedly. An example of compiled data is:
Part Number: Measurment 1: Measurement 2: Measurement 3
1 9.160132479 3.208232519 8.725015854
2 10.09989868 5.35886652 8.353012516
3 11.5960797 10.72768738 12.12945402
4 11.1971081 11.00897504 8.142467291
5 7.725476076 10.30067651 10.76296998
6 13.53243557 15.09578684 10.1430507
7 8.805311215 11.80606734 8.751404916
8 7.152713146 5.028629116 12.11245612
9 12.32607212 6.355632668 9.221960706
10 10.22083684 3.704164112 10.25662496

In a Gage R&R study the differences between the measurements are generally very small so it is best to measure out to eight decimal places for accuracy (see Reference 2).

Calculate the average for each group. Use a spreadsheet to automatically calculate this formula or do it with a calculator. For a manual calculation, compute the average for each group by adding all the observations in that group, divided by the total number of observations. For example, in column one, the sum of all the observations is 101.8160639. If you divide 101.8160639 by 10, which is the total number of observations in this group, you get 10.1816064. Apply the same formula for the other two groups, obtaining 8.259471804 and 9.859841707, respectively.

Calculate the standard deviation for each group, using a spreadsheet program or manually. For a manual calculation, take each observation or "X" and subtract it from the mean of that group. Square each of these values by multiplying it by itself. Take the sum of all the squared values and divide by the total number of observations in that group, minus one. Take the square root of this final number. For the first group, a table of the values is:

X: Average: X-Average: (x-Average) ^2
9.160132479 10.1816064 -1.0214739 1.043408971
10.09989868 10.1816064 -0.0817077 0.006676152
11.5960797 10.1816064 1.4144733 2.000734723
11.1971081 10.1816064 1.0155017 1.031243703
7.725476076 10.1816064 -2.4561303 6.03257617
13.53243557 10.1816064 3.3508292 11.2280561
8.805311215 10.1816064 -1.3762952 1.894188437
7.152713146 10.1816064 -3.0288933 9.174194347
12.32607212 10.1816064 2.1444657 4.598733213
10.22083684 10.1816064 0.0392304 0.001539027

The sum of the final column is 37.01135084. This number divided by 9 is 4.112372316 and the square root of 4.112372316 is 2.027898497. Apply the same formula for the other two groups, obtaining 4.0259467 and 1.4690118, respectively.

Square the standard deviation of each group to obtain the variance. For group one, 2.0278985 multiplied by itself is 4.112372316. Apply the same formula for the other two groups, obtaining 16.20824682 and 2.157995538, respectively.

Calculate the average variance for all the groups. For example, 4.112372316 + 16.20824682 + 2.157995538 is 22.47861. This value is divided by the total number of parts, which is 30. The value is 0.749287.

Obtain the standard deviation for all the groups by calculating the square root of the average variance. For example, the square root of 0.749287 is 0.8656137.

Calculate tolerance by subtracting the upper specification limit from the lower specification unit. The specification units are determined by the manufacturer and refer to the amount of error they are willing to tolerate in their manufacturing process and still make a profit. For example, if the measurement device cannot over-measure by more than 4.1 inches, the upper specification limit is 4.1 inches. If the measurement device cannot under-measure by more than (-2.1) inches, the lower specification limit is (-2.1) inches. The tolerance would then be 4.1-(-2.1) which is 6.2.

Divide the standard deviation multiplied by the standard deviation spread for all groups by the tolerance. Multiply this value by 100. For example, 0.8656137/6.2 equals 0.139615113. Multiply this value by 100 to equal 13.9 percent.