# Gage R&R for quantitative data in Excel tutorial

This tutorial shows how to compute and interpret a Gage R&R for quantitative data analysis in Excel using the XLSTAT software.

## Dataset for Gage R&R: control and validate your measurement method and systems, when having several quantitative measures taken by one or more operators on several parts

The data are from [Montgomery, D.C. (2001), Introduction to Statistical Quality Control, 4th edition, John Wiley & Sons].

They correspond to a measurement system analysis with 10 parts, 3 operators and 3 repetitions for each measurement.

## Goal of this tutorial

Measurement System Analysis (MSA) or Gage R&R (Gage Repeatability and Reproducibility) is a method to control and judge a measurement process. It is useful to determine which sources are responsible for the variation of the measurement data. Variability can be caused by the measurement system, the operators or the parts. Gage R&R applied to quantitative measurements is based on two common methods: ANOVA and R control charts.

The word "gage" (or gauge) refers to the fact that the methodology is aimed at validating instruments or measurement methods.

When the measures are quantitative data, two alternative methods are available for Gage R&R analysis. This first is based on analysis of variance (ANOVA) and on R control charts (Range and average).

A measurement is "repeatable" if the measures taken by a given operator for the same object (product, unit, part, or sample, depending on the field of application) repeatedly, do not vary above a given threshold. If the repeatability of a measurement system is not satisfactory, one should question the quality of the measurement system, or train the operators that do not obtain repeatable results if the measurement system does not appear to be responsible for the high variability.

A measurement is "reproducible" if the measures obtained for a given object (product, unit, part, or sample, depending on the field of application) by several operators do not vary above a given threshold. If the reproducibility of a measurement system is not satisfactory, one should train the operators so that their results are more homogeneous.

The goal of a Gage R&R analysis is to identify the sources of variability and to take the necessary actions to reduce them if necessary.

## Setting up the analysis of a measurement method with several quantitative measures obtained by several operators on several parts

Once XLSTAT is activated, select the **XLSTAT** / **SPC** / **Gage R&R quantitative** command.

The SPC Gage R&R dialog box will appear. Then select the data on the Excel sheet.

Select the column "Measurement" as **Y / Measurement**s, the column “Operator” as **X / Operator**, and the column "Part” as **Parts**.

Activate the **Variable labels** option as the first row of the selections contains the variable names.

In the **Options/Model** tab, select the ANOVA method. Then, enter the value 6 as **k sigma i**n order to define the variance of the study as 6 times the global standard deviation of the sample, and select the **crossed ANOVA**.

In the **Options/Estimation** tab, select the R-bar option.

In the **Outputs** tab as well as in the **Charts** tab, activate all options.

## Interpreting the results of a Gage R&R quantitative analysis

The first results are the variance components together with its chart. You can see that the biggest part of the variance is caused by variation between parts (96.4% of the variance). The measurement system has a very low contribution to the total variance (3.6%), and it can therefore be qualified as capable.

The following tables give details on the distribution of the variance and the derived key indicators. We can see that the **Signal to noise** ratio is adequate.

If the ANOVA method has been selected like in this tutorial, then the results of the ANOVA with its GOF indicators and the table with the variance analysis are displayed. Look at the p-values to assess the significance level.

The following tables are used to build the **X-bar control chart** including the different control limits and central lines.

In the first table the data of the X-bar control chart starting with the group mean, group min and group max are displayed. After this the central line (CL), the lower (LCL) and the upper (UCL) control limit and the lower and upper zone limits for the A and B assessors are displayed for each group.

The X-bar control chart sums up all the information above. The mean group values are not between the lower and upper control limits. The variance between the parts is not under control.

Like the X-bar chart the data of the **R chart** are always inside the control limits and no special causes are present. This is a typical result of a measurement system analysis.

Both control charts let us come to the conclusion that the measurement system is capable and that the variance of the parts is not under control.

The following charts show **box plots and scatter grams for each operator and for each part**. They provide a visual comparison of the different distributions.

We can see that the variation between the parts is important. The parts 2, 4, 6 and 8 have clearly higher measurement values than the parts 3, 5, 7 and 9.

The variance between the operators is very small. No differences are visible.

## Conclusion

This tutorial therefore concludes that the measurement system is capable but that the variance between parts is not under control.

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