Use a nested gage R&R study to evaluate the repeatability and reproducibility of a measurement system used to measure a continuous variable. A nested gage R&R study is used when parts cannot be measured multiple times by multiple appraisers, for example, destructive testing in which the homogeneous batch size is too small to accommodate multiple tests by multiple operators. This analysis requires that you choose groups of parts similar enough so they can be considered the same part; otherwise, the part variation will mask the measurement variation. You should answer the question of whether you can trust your data before you calculate a baseline or attempt any improvement.
Answers the questions:
- Can I trust my data (applies to both inputs and outputs)?
- Is the measurement system capable of evaluating process improvements?
|When to Use
|Start of project
||Verify you can precisely measure process outputs before attempting to perform a baseline analysis.
||Verify you can precisely measure process inputs being investigated.
|End of project
||Verify you precisely measure process outputs after improvements have been made. It is not uncommon to reduce variation to a point where you cannot do so with the pre-improvement measurement system.
|End of project
||Verify you can precisely measure critical process inputs that must be controlled to maintain the improvements. These should have been already verified earlier in the project.
Your data must be continuous Y with two X-variables (typically operator and part); typically for destructive testing evaluation.
- Typical standards for %R&R (% study variation, % tolerance, and % process) are:
- <10% - The measurement system is acceptable.
- 10% to 30 % - The measurement system is acceptable depending on the application, the cost of the measuring device, cost of repair, or other factors.
- >30% - The measurement system is unacceptable and should be improved.
- The main purpose of measurement systems analysis in the context of a process improvement project (Six Sigma, DMAIC, and so on) is not to determine whether the measurement system can sort good from bad (Is it acceptable for inspection purposes?). Rather, its purpose is to discover whether the measurement system can see the process clear enough that, if you make a change, that change will be visible (Is it acceptable for process improvement activities—that is, DMAIC?).
- The key metrics are, therefore, % study variation (%SV) or % process (SV/Process). Both metrics evaluate the ratio of the standard deviation of the measurement system to the standard deviation of the total process. The difference is % study variation uses the standard deviation of the sampled parts as the estimate of the process standard deviation while % process requires a user-entered estimate (historical) of the process standard deviation.
- If you use % study variation to validate your measurement system, you must first verify that the study samples mimic the actual process profile. For example, if you pulled from production all parts that exceeded the upper specification limit in the study, the standard deviation of those parts would likely be very small compared to that of the entire process.
- If you want to evaluate whether the gage system is acceptable for inspection purposes, use % tolerance.Note: In a gage R&R study, tolerance is defined as the difference between the upper and lower specification limits. You must enter tolerance to calculate this metric.
Example and Comments
Study Var %Study Var %Tolerance %Process
Source StdDev (SD) (6 * SD) (%SV) (SV/Toler) (SV/Proc)
Total Gage R&R 0.30237 1.81423 27.86 15.12 43.20
Repeatability 0.19993 1.19960 18.42 10.00 28.56
Reproducibility 0.22684 1.36103 20.90 11.34 32.41
Operator 0.22684 1.36103 20.90 11.34 32.41
Part-To-Part 1.04233 6.25396 96.04 52.12 148.90
Total Variation 1.08530 6.51180 100.00 54.26 155.04
Number of Distinct Categories = 4
Notes on the above table
- % study variation is the ratio of the standard deviation of the measurement system divided by the standard deviation of the sampled parts. With a value less than the suggested maximum limit of 30%, this value is marginally acceptable.
- However, using the historical estimate of the process standard deviation, a % process of 43.2% tells us that the measurement system is not acceptable to evaluate process improvements. Note: For this column to appear, you must enter a historical estimate of the standard deviation. When % SV is significantly different than SV/Process, as in the case above, the chosen sample of parts does not mimic the profile of the actual process and % SV is unreliable.
- % tolerance of 15.12% is well below the desired limit of 20% and you can use your measurement system to safely sort products into good and bad categories. Note: For this column to be shown, you must enter the tolerance band or width.
- The number of distinct categories is related to the standard deviation of the chosen samples. If, as in this case, the samples do not reflect the actual process profile, ignore this metric.
- If you have discrete numeric data from which you can obtain every equally spaced value and you have measured at least 10 possible values, you can evaluate these data as if they are continuous.
- Obtain a suggested minimum of 10 groups of parts/process outputs that cover the expected range of output.
- As a suggested minimum, each group should consist of at least six parts to allow two trials for each of three appraisers.
- Select a minimum of two qualified appraisers.
- Split the selected parts into groups. Each appraiser will take multiple measurements on their group of parts. The testing may be destructive, in which case the appraisers may break each part into subparts in order to take multiple measurements.
- Have each appraiser evaluate their parts (preferably with the parts being presented randomly for measurement).
- Repeat this cycle two or more times (number of trials).
- In Minitab, enter the measurement in one column, the appraiser in a second column, and the part in a third column. Analyze the measurements.
- To evaluate whether the gage can be used for inspection, you must enter a tolerance width.
- If the variation in your samples is not representative of the variation in the process, enter a historical standard deviation.
For more information, go to Insert an analysis capture tool.