**Gage R&R with Automated Gages**
This has come up before in a similar vein. The dissimilarity is that process instruments are 'continous'. But, something to think about anyway... See

Gage R&R Studies for Process Monitoring Instruments?
What we're talking about is doing an R&R with only 1 R.

Which in part reads:

With CMMs, the measurement process is independent of operator technique and the digital readout does not need to be interpreted as with analog scales. In this case, the definition of an appraiser must be broadened from the traditional GR&R operator to include any measurement system. If a measurement process uses only one automated test system without an operator to impact the test, the resulting appraiser variation (AV) component has little or no meaning, because variation wasn't caused by an appraiser taking measurements. Only the equipment variation (EV), which is variation caused by the measurement equipment, is of consequence.

If substantial variation results from placing parts in a fixture, then the GR&R study should address it in a more comprehensive way. This would involve repeatedly placing the same part in a fixture and obtaining a single reading for each repetition.

Gathering the data

CMMs typically measure on one to three axes and can incorporate video, laser or touch probe sensors. Although the sensors operate differently, the technique for gathering data for the GR&R study is the same. The steps for gathering the data are:

1. Select a part or parts on which to perform the study.

2. Use only one CMM and one mode of measurement if it has multisensor capability.

3. Measure each part from two to 10 times, preferably as many as 25 times if using automated testing equipment and one part. As a rule of thumb, "part-times-trial" combinations should always be at least 25 to gather a reasonable amount of data for analysis. The more measurements the better.

4. Record measurements and perform calculations using the GR&R calculation method. Overall variation and between-subgroup variation standard deviation calculations are not recommended because they exaggerate the standard deviation for processes that are not in statistical control. A prerequisite for all GR&R studies is that the measurement process is in statistical control.

Selecting a calculation method

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 * sigma / c4) / (USL - LSL))*100 or % GR&R = ((6 * sigma / 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.

Example

To gather data for one study, an optical and touch probe CMM was selected. The Programmable CMMs offer increased flexibility and efficiency in the inspection areas and shop floor by providing the ability to run inspection routines with minimal operator intervention. The programmable test feature was used to save time taking measurements. The automatic test feature, programmable in a language called QVBASIC, is activated by a mouse click and it does repeated measurements automatically, using the axis or measurement sensor required for the test.

From the 25 repeated measurements on the part, a standard deviation of 0.1 microns (µm) was obtained. The USL was 35 µm and our LSL was 25 µm.

Using the previous formula, % GR&R = ((6 * sigma / c4) / (USL - LSL))*100, and substituting the values, % GR&R = ((6 * 0.1 / 1) / (35.0 - 25.0))*100.

The result of these calculations are: GR&R = 6%.

No hard and fast rules are set for determining the acceptable part tolerance that is lost to gaging error, but marginal manufacturing processes generally require better gaging because the manufacturing process takes up much of the tolerance. In other cases, the tolerance is small and only a small percentage is acceptable. Generally, the following guidelines are accepted, but they are subject to supplier requirements:

* If the GR&R as a percent of the tolerance is 10% or less, the gaging system is acceptable.

* If the GR&R as a percent of the tolerance is between 11% and 29%, the gaging system may or may not require further analysis to find the source of the error.

* If the GR&R as a percent of the tolerance is 30% or greater, the gaging system requires further analysis to find the source of error.