For decades now, the measurement systems analysis (MSA) approach has been the predominant method for evaluating measurement systems capability. Although this method is widely considered to be an acceptable and comprehensive approach throughout most of the world, a growing number of specialized industries, both overseas and in the United States, have begun to adopt a different system based on the measurement uncertainty approach.
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A substantial minority of manufacturing companies use the measurement uncertainty approach, including many in aerospace, European automakers, their suppliers, and companies that certify under ISO 17025, among others. If you think it might be a better way to go, are just curious, or perhaps wish to certify certain gauges that you use to calibrate other gauges, read on. This article will describe what is different about the procedures, tell you where to get manuals which govern the measurement uncertainty approach, and provide an example using popular software.
What is different about the procedures?
"Everyone" uses the Measurement Systems Analysis, Fourth Edition (MSA 4) published in 2010 by the Automotive Industry Action Group. The manual describes the basic studies that everyone uses, which are bias, linearity, stability, and gauge R&R (repeatability and reproducibility). MSA 4 also describes a procedure for determining measurement capability that we called the MSA approach.
The procedure for the MSA approach is as follows:
1. Start with a gauge R&R study done in the production environment.
2. Calculate a measurement capability statistic, usually gauge R&R percent tolerance or an alternative such as number of distinct categories. (This article will use percent tolerance statistics, which are easy to calculate and common to both procedures.)
3. If the decision isn't clear, do further studies for information purposes: bias, linearity, stability or a combination of these, done in the calibration environment.
The procedure for the measurement uncertainty approach has two parts:
A. In the calibration environment
1. Perform one or more studies: bias, linearity, or stability.
2. Summarize and combine the results using a form called an "uncertainty budget."
3. Calculate resolution percent tolerance and calibration-uncertainty percent tolerance. If they pass, go to part B.
B. In the production environment (real parts, real operators, real conditions)
1. Perform a gauge R&R study using the analysis of variance (ANOVA) calculation method.
2. Enter the additional standard uncertainties into the existing uncertainty budget.
3. Calculate measurement-uncertainty percent tolerance or an alternative statistic (Cg, etc.).
Discussion of procedure differences
The MSA procedure usually makes the decision to accept a gauge for a particular application without any data about how the gauge performs in the calibration environment. The maximum allowance is 30 percent for GRR percent tolerance.
The measurement uncertainty procedure will always include uncertainty contributors from both the calibration environment and the production environment. The maximum allowance is 30 percent of tolerance based on expanded uncertainty.
You might expect the measurement-uncertainty method to give you worse results, but the opposite is true. The numerator of the GRR percent-tolerance formula has a large effective multiplier. Often the larger multiplier, six instead of four, more than makes up for the smaller number of uncertainties included.
Where are measurement uncertainty procedures documented?
In 2011 the German Association of the Automotive Industry (VDA) published Capability of Measurement Processes, Vol. 5. Examples are included. More detail on basic uncertainty budgets and gauge capability formulas is available in ISO 22514–7:2012—"Statistical methods in process management." For information about the studies used to generate the numbers, see MSA 4. These manuals are available in multiple languages.
Example of measurement uncertainty procedure
The following example is from VDA 5, Annex F.1, on page 111. The procedure in the VDA 5 manual starts by choosing what the manual calls a "type 1" study, meaning bias, linearity, or stability. The results will be listed first on the uncertainty-budget form; there will be one gauge, one operator, and one reference standard unless the linearity study is chosen. (Linearity requires three or more reference standards.) Figure 1 shows the data for this linearity study example. It has been entered into GAGEtrak software for analysis. Figure 2 shows part of the analysis.
Preliminary uncertainty budget
In figure 3, GAGEtrak has provided a preliminary uncertainty budget using traditional estimators, but the user can review the calculations, charts and certificates, and edit the uncertainty budget as needed.
The human touch
Interpretation of the linearity and bias analysis and the linearity chart concluded there was no systematic error from either linearity or bias. However, bias was behaving like a random variable. Figure 4 reflects the following editing decisions:
1. Linearity: Deleted the plus or minus value
2. Bias: Changed the plus or minus value to the maximum absolute value of Avg. Bias per Part found in figure 2 and selected a rectangular "safe choice" probability distribution
3. Resolution: Verified the resolution number is correct and changed the divisor to 3.464 (recommended by the manuals)
4. Reference standard: Entered from the certificate
Calibration-uncertainty percent tolerances
1. Resolution percent tolerance = 100 (resolution/tolerance) = 100 (0.0001/0.005) = 2.00%
2. Calibration-uncertainty percent tolerance = 100 (2 x expanded uncertainty/tolerance) = 100 (2 x 0.000202/0.005) = 8.08%
3. Record these capabilities on the uncertainty budget as shown in figure 4.
4. These capabilities meet the recommendations of-5 percent maximum and 15-percent maximum, respectively.
The next step is to do a study in the production environment. This would usually be a gauge R&R study. A report showing the data and calculations for this study is shown in figure 5.
Completed uncertainty budget for measurement uncertainty
Here we used the copy-and-paste function to create a duplicate uncertainty budget. If necessary, the calibration items can be summarized to take up less room. Then we added the uncertainty contributors from gauge R&R found in figure 5. If necessary, we would have added contributors from uncontrolled temperature, as seen in figure 6. Included items were as follows:
1. Repeatability on test parts
2. Reproducibility
3. Interaction
Final step is to determine the measurement process capability
1. Measurement-uncertainty percent tolerance = 100 (2 x expanded uncertainty/tolerance) = 100 (2 x 0.000406/0.005) = 16.24%
2. Record this capability on the uncertainty budget as shown in figure 6.
3. This capability meets the recommendation of 30-percent maximum.
Comparison of alternative methods
Results with measurement uncertainty method:
1. Resolution percent tolerance = 2.00%, maximum 5%
2. Calibration-uncertainty percent tolerance = 8.08%, maximum 15%
3. Measurement-uncertainty percent tolerance = 16.24%, maximum 30%
Results with the MSA method (using only GRR percent tolerance, as shown in figure 5):
Gauge R&R percent tolerance = 21.09%, maximum 30%
Because of the larger multiplier used by Gauge R&R percent tolerance, you would more often have difficulty meeting the stated requirement. The benefit is that you could usually skip the calibration uncertainty study, unless the gauge will be used to calibrate other gauges. However, the burden of performing calibration uncertainty studies may be less than you imagine. For example, suppose company X has 300 micrometers of a certain type which are used for 50 different part characteristics. They would potentially require as few as one master calibration study and uncertainty budget. (We choose reference standards to be similar to center of tolerance. That may result in additional calibration studies.) Eventually, they would use copy-and-paste to create 50 uncertainty budgets for measurement uncertainty, each customized for an individual part characteristic.
A tip for future use
The most popular study to use for calibration uncertainty is a bias study with one reference standard and 25 repetitions. The software that we used for this article, GAGEtrak, can do bias studies in two different places—in the linearity module or in the stability module. The linearity module is more convenient because it has the uncertainty budget, but if you also want a short-term stability study, just enter the same data into the stability module.
Gary Phillips is a measurement systems consultant for CyberMetrics, a Quality Digest content partner.
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