## About this lesson

Variable data Gage R&R Studies calculate a comprehensive measurement that can be used to determine the efficacy of the measurement system that is creating variable measurements of product or process characteristics. This lesson describes those calculations and highlights where weaknesses in the system will be exposed.

## Exercise files

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Variable Data Gage R&R Calculations.xlsx10.5 KB Variable Data Gage R&R Calculations - Solution.xlsx

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## Quick reference

### Variable Data Gage R&R Calculations

Variable data Gage R&R Studies calculate a comprehensive measurement that can be used to determine the efficacy of the measurement system that is creating variable measurements of product or process characteristics. This calculation can be done with an ANOVA analysis or with the Means and Ranges approach which will be demonstrated.

### When to use

If you are conducting a variable data Gage R&R you will need to use one of the two methods for calculating the results. The Means and Ranges method shown is much simpler than the ANOVA method which requires a statistical analytics application.

### Instructions

Variable data always provides a richer analysis than attribute data because small changes are detectable and meaningful information is found within them. There are two analytical methods that can be used for variable data Gage R&R analysis. They provide similar answers.

The ANOVA method requires sophisticated statistical software. It identifies both main effects and secondary effects, giving a very accurate and thorough understanding of the measurement system variation. The Means and Ranges method is much simpler and can be calculated with a few equations and some statistically derived constants. It is not quite as accurate, but can be quickly calculated using a basic spreadsheet such as Excel.

The Means and Ranges methodology equations are provided. Even if using the ANOVA approach, an understanding of the Means and Ranges equations will provide a better understanding of the ANOVA results. Both approaches calculate a series of component variation to determine the total system variation and the Gage Repeatability and Reproducibility (GRR) value for the measurement system.

- Part Variation (PV) is based upon the overall variation in parts as tested in the Gage R&R Study. It uses the mean value for largest and smallest item in the study. The K constant varies based upon the number of items in the study. The value for the K constants is shown below.
- Equipment Variation(EV) represents Repeatability. It is the variation within an individual appraiser’s measurements. Therefore, it is the variation due to everything except the appraiser. To calculate this variation, you must first calculate the range for each item with each appraiser. Then take the average of the ranges for each appraiser. Finally, take the average of the appraiser’s average range. The K constant varies based upon the number of trials. The value for the K constants is shown below.
- Appraiser Variation (AV) represents Reproducibility. It is the variation between the appraisers. It uses the mean value for the appraisers across all the items and trials. The formula is the most complex. It starts with the highest appraiser mean and the lowest appraiser mean. It takes the difference of those multiplies times a constant that is based upon the number of appraisers and then squares that value. From that value it subtracts the Equipment Variation (EV) squared and divided by the number of trials and items. If that value is a negative number, the AV is zero. If it is a positive number the AV is the square root of that value. The value of the constant is shown below.
- Total Variation (TV) is just that. It combines the PV, EV and AV by taking the square root of the sum of the squares.

- GRR is the just the Repeatability and Reproducibility portion of the total variation. It is normally expressed as a percentage of the total variation.

As mentioned before, a GRR of less than 10% is acceptable, a GRR between 10% and 30% is marginal and anything else is unacceptable.

- K Constants have been statistically derived and necessary for use with Means and Ranges form of calculating the variable data Gage R&R Study results.

### Hints & tips

- Collect your data then calculate the appropriate means and ranges in your spreadsheet. Then use those values in the equations.
- Variable data Gage R&R Studies normally have at most 3 appraisers, 3 trials, and 20 items for measurement. If you use more than these, you will need to use a statistical lookup table to find the values of the constants that are appropriate for your study.

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