# Unbalanced Designs and Gage R&R (Expanded)

Last week, a customer called with an issue related to running a Gage R&R nested design in Minitab Statistical Software. Everything initially looked okay, as he had the three columns necessary to perform a successful study: one for parts, one for operators, and another for the measurements. However, when he tried to analyze his data using **Stat > Quality Tools > Gage Study**** > Gage R&R (Nested)**, he would get this error message:

**Gage R&R Study - Nested ANOVA **

* ERROR * Design is not balanced; execution aborted.

One of the assumptions in performing a Nested Gage analysis is that the data is balanced, meaning that it has an equal number of observations for all possible combinations of the factor levels. In a balanced Gage Study, each operator will measure the same number of parts the same number of times. When you have an unbalanced design, you have an unequal number of observations for the Operator/Part combinations.

I showed the customer how to validate this error message by going **to Stat**** > Tables > ****Cross Tabulation and Chi-Square.** He put his** Part** column under ‘For Rows’ and his **Operator** column under ‘For Columns’, and then simply hit ‘OK’ in the dialog window. Here are the results:

**Tabulated statistics: Part, Operator **

Rows: Part Columns: Operator

A B C D E F All

1 21 21 21 21 21 42 147

2 21 21 21 21 21 42 147

3 21 21 21 21 21 42 147

All 63 63 63 63 63 126 441

Cell Contents: Count

It looks like Operator F measured twice as many parts compared to any other operator.

In some cases, this Gage Nested error can be quite useful. It can reveal to the user that he has an accidental missing measurement in his design or possibly a duplicate row that he needs to remove. However, in this caller's case, these were legitimate measurements that he wanted to analyze. How did we get around this?

Fortunately, Minitab has another Gage tool that can analyze unbalanced data for either Crossed or Nested designs. I instructed the customer to go to **Stat > Quality Tools > Gage Study ****> Gage R&R (Expanded)**. The dialog window for this tool may look intimidating, but the rules remain the same: you still need to enter in columns for **Part, Operator, **and **Measurements**. There is one more thing that we have to add before hitting ‘OK’ to analyze the design. Because the customer was trying to analyze a nested design, we had to add **Parts(Operators)** under the box entitled ‘Nesting.’ See the example below:

As you can see from the picture above, Gage Expanded allows for ‘Additional factors’ beyond Operator and Part. (All of the ‘Additional factors’ are assumed to be random factors unless specified in the ‘Fixed factors’ field as well.) Pretty powerful tool, right? For more information on our Gage R&R Expanded menu, click on the Help button shown in the picture above, or go to **Help**** > Help ****> Stat Menu ****> Quality Tools ****> Gage R&R Expanded**.

I hope this helps you the next time you run a Gage analysis in Minitab!

Name: Mark Goldstein• Monday, March 5, 2012I work for a company that is using Minitab 12. I don't see GR&R nested as an option. do you have a recommendation (other than upgrade the software)? is there a way to do a nested study in this earlier version of Minitab?

Name: Andy Cheshire• Thursday, March 8, 2012Hi Mark!

Thanks for your comment! There is one workaround that can be done in order to analyze a nested design. You would have to go to our Stat-->ANOVA menu select either 'Fulled Nested ANOVA' or 'General Linear Model'.

1. If you use a Fully Nested ANOVA, then list your Operator first, then your Part column.

2. If you use a General Linear Model, the order of how your list your factors in the model box do not matter, as all you need to list is: Part(Operator) Operator

Unfortunately, the downside to using ANOVA menus is that they don't visually break down the Variance Components as well as our Gage R&R tables do. Thus, a bit of investigation needs to be done to find what the VarComp values are. Follow the template below and you'll be able to find your values:

1.the VarComp for 'Part-to-Part' under Gage can be found in ANOVA as 'Part' in the Variance Components table.

2.The VarComp for 'Reproducibility' under Gage can be found in ANOVA as 'Operator' in the Variance Components Table.

3. the VarComp for 'Total Gage R&R' would then be 'Error' under MSE under the ANOVA table.

I hope this helps!

Name: Mike• Wednesday, May 9, 2012Hello,

I am using Minitab 15 and I am trying to run a nested study but I receive the error of:

Gage R&R Study - Nested ANOVA

* ERROR * No replications - cannot calculate statistics; execution aborted.

I also have equal sample sizes for each operator. Any help would be appreciated.

Thank you,

Mike

Name: Andy Cheshire• Thursday, May 17, 2012Hi Mike!

I would recommend seeing if each operator measured each part at least twice. Once this has been verified, your analysis should go through successfully. Give us a call if it doesn't! 814-231-2682.

Name: Marcelino Nino• Tuesday, May 22, 2012Hello

I want to run GR&R for destructive part with only One operator but

I don't know how is the format that I have to use. I try to run with normal format but requiere at lest 2 operators.

Thanks

Name: Andrew Cheshire• Friday, May 25, 2012Hi Marcelino,

Thank you for your question. Unfortunately, Gage Nested will require at least 2 operators. If you are interested in running a Gage Study with one operator, please take a look at our Type 1 Gage Study found under Stat->Quality Tools->Gage Study. If you have further questions, please feel free to give us a call at 814-231-2682.

Name: Dimitri• Tuesday, August 28, 2012Hi Andrew,

I have a question, I am using Minitab 15, the expanded feature does not seem to be available.

I have a gage study that is 'semi' destructive. In that it's a destructive test and the measurement happens in real time, so repetitions per part are not possible. However, the measurement is visual, so there are multiple operators able to evaluate the same part. I've tried both nested and crossed and it I get the:

* ERROR * No replications - cannot calculate statistics; execution aborted.

Any thoughts?

Thanks,

Dimitri