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!