XLSTAT: GR&R for Quantitative Data in Excel

 

Background

Measurement System Analysis (MSA), or Gage R&R, evaluates a measurement process by identifying sources of variation—whether from the system, operators, or parts. For quantitative data, Gage R&R uses ANOVA and R control charts.

"Repeatability" means a single operator’s measurements on the same item vary minimally; poor repeatability suggests issues with the system or operator training.

"Reproducibility" means measurements from different operators on the same item vary minimally; poor reproducibility indicates a need for operator training to ensure consistency.

The goal of Gage R&R analysis is to identify sources of measurement variability and take corrective actions to reduce them if needed.

 

Dataset for Example

The attached 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.

 

Setting Up

• Open XLSTAT.

• Click on the Quality/ Statistical Process Control menu and select the Gage R&R quantitative feature.

• The SPC Gage R&R dialog box will appear. 

In the General tab: 

• 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.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

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.

The Signal to noise ratio is adequate.

When the ANOVA method is selected, the results of the ANOVA with its GOF indicators and the table with the variance analysis are displayed. The p-values allow us to assess the significance level.

The tables provide data for the X-bar control chart, including:

• group means, minimums, maximums
• central line (CL), lower (LCL) and upper (UCL) control limits
• zone limits for A and B assessors.

The X-bar chart shows mean group values falling outside control limits, indicating that variance between 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 indicate the measurement system is capable, but 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.

The variation between the parts is important. 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.

We can conclude that the measurement system is capable, but part-to-part variance is not under control.