In expanded Gage studies, we are interested in including more than just an operator or part as factors in the Gage R&R. This is especially useful if the study is interested in investigating the differences across measurement devices, different labs, or even locations.
Here, we will look at a Gage R&R including one extra factor, a preparation method effect on the sample. In this recipe, the study looks at the force required to remove adhesive from a glass plate. The sample is a batch of adhesive, and the response is the force required to remove a test piece from a glass plate. Two operators prepare the samples and test the force of the adhesive.
Additionally, in this study, three different preparation methods are used to clean the glass plates before the adhesive is applied.
We will use the expanded Gage R&R to look at the effect of the preparation method, operator, and adhesive batch on the force measurements.
The worksheet contains the columns Preparation Method, Sample, Operator, and Force (N).
The preparation method will be identified as an additional component to the part-to-part variation.
- Open the worksheet
Gage R&R Expanded.mtwby using Open Worksheet from the File menu. - Navigate to Stat | Quality Tools | Gage Study and select Gage R&R Study (Expanded).
- Enter the columns into the dialog box as shown in the following screenshot. Enter
Samplein Part numbers,Operatorin Operators:,'Force (N)'in Measurement data,'Preparation Method'should be entered into Additional factors and Fixed factors.
- Click on the Terms button.
- From the Include terms in the model up through order drop-down list, choose 2 to select all two-way interactions.
- Click on the Part-to-Part Variation button.
- Move Preparation Method and the Sample*Preparation Method interaction to the selected terms.
- Click on OK.
- Click on the Graphs button.
- Enter
'Preparation Method'into both the sections for Plots of measurements by single factors and Plots of average measurements by two factors. - Click on OK in each dialog box to run the Gage R&R.
By entering the preparation method as an additional factor, we look at the effect of the three preparation methods on the measurements. With the expanded Gage R&R tools, factors are by default set to random factors, unless defined as fixed. As the preparation method is a choice of the three techniques, we are interested in finding the mean effect of each preparation method rather than the variation from the population of methods. Hence, we define the preparation method as a fixed factor.
With parts in a study, these are expected to be random as these are a random selection of samples from the larger population. Operators are also by default set to random factors, as the operators are assumed to be a small selection of operators in the population, and we wish to find the variation across the population of operators. The expanded Gage R&R study allows us to define operators or parts as fixed, unlike the crossed or nested studies, although it is unlikely that parts in a Gage R&R will be fixed.
The option Terms is used to identify which terms to include in the study. By entering all two-way interactions, we can look at the effect of Sample*Operator, Preparation Method*Sample and Preparation Method*Operator.
The study will automatically remove interactions that have a P-value greater than 0.25, this Alpha to remove interaction can be changed from within the Options button if required.
As the preparation method may affect the sample, it has been included as a part-to-part variation. If we had additional factors that contribute to the measurement rather than to the sample, these would be left as measurement system variations.
We are also able to choose the charts to be displayed. The Graphs option is used to include the charts for Preparation Method and the two-factor interactions, including Preparation Method. Xbar-R charts can also be included for additional factors.
The expanded study can allow us to include nested factors as well. Consider comparing measurements across two different laboratories; we would nest operators within each lab.