Gage R&R Study (Crossed)


Evaluates the repeatability and reproducibility of a measurement system used to measure a continuous variable. To use this tool, multiple operators must be able to measure all parts used in the study multiple times. 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 Purpose
Start of project Verify you can precisely measure process outputs before attempting to perform a baseline analysis.
Mid-project Verify you can precisely measure process inputs that you are investigating.
End of project Verify you precisely measure process outputs after improvements have been made. It is common 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 need to be controlled to maintain the improvements. These should have been already verified earlier in the project.


Continuous Y, two X-variables (typically operator and part).


  1. Obtain a suggested minimum of 10 parts/process outputs to cover the expected range of output.
  2. Select a minimum of two (preferably three or more) qualified operators.
  3. Tell the first operator to evaluate the parts (preferably with the parts being presented randomly for measurement).
  4. Repeat for each operator.
  5. Repeat this cycle two or more times (number of trials).
  6. In Minitab, enter the measurement in one column, the operator in a second column, and the part in a third column. Analyze the measurements.
  7. To evaluate whether you can use the gage for inspection, you must enter a tolerance width.
  8. If the variation in your samples is not representative of the variation in the process, enter a historical standard deviation.


  • Typical standards for %R&R (%Study Var, %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 so, 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 Var (%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 Var 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 Var to validate your measurement system, you must first verify 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 one wants to evaluate whether the gage system is acceptable for inspection purposes, %Tolerance is used. Note: The tolerance used in the gage R&R study is defined as the difference between the upper and lower specification limits and must be entered for this metric to be calculated.

Examples 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 Var 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.
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