One method to evaluate CMM performance is to conduct a gage repeatability and reproducibility (GR&R) study. GR&R studies focus on identifying and eliminating measurement variation caused by out-of-calibration gages, environmental conditions, methods or procedures and appraisers, commonly referred to as operators. By using GR&R studies, measurement variation can be identified and reduced to produce more precise measurements. Ultimately, reducing measurement variation results in a greater ability to differentiate between parts that are in or out of specification. Measurement variation adds to the total variation seen when products are assembled, and this variation makes a manufacturing process appear less capable.

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 Arial, 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 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 (Km) was obtained. The USL was 35 Km and our LSL was 25 um.

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.

**More information**

This is a simple method to verify that for a single part, the CMM can meet a company's needs. However, because of the large distances CMMs can measure and the volume created by measurements in the X, Y and Z axes, the potential for measurement errors is great. The American Society of Mechanical Engineers (ASME) CMM standard contains many tests that explore these issues. Briefly, some measurement considerations that may be explored include:

- Are there measurement and variation differences along axes?

- If not using the entire stage, are the measurements and variation different depending on part location on the stage?

- If the CMM has multiple measurement sensors, such as video, touch probe, or laser, does one of them work better for a particular measurement?

- Does changing the light source or illumination angle improve edge detection in video mode and decrease measurement error?

If the answer is yes to one or more of these questions, more than one measurement system is appropriate. For example, if multiple sensors are employed, then measurement variation is potentially different for each sensor. Because of this, each sensor is considered a separate measurement system. Therefore, apply a GR&R study that involves more than one appraiser.

The ASME also has a detailed standard for evaluating a CMM. The standard, Method for Performance Evaluation of Coordinate Measuring Machines, ASME B89.1.12M-1990, provides information on evaluating CMM performance in more detail than a GR&R study. The ASME standard provides many tests to verify CMM performance as well. Combined with the information in the article and the ASME standard, users can gain insight needed to understand a CMM's capabilities and limitations.