OK, I don't know if this will all fit - if not, I'll continue it in another post. I had this in Word already so I'm copying it here:
Gage R&R Using MINITAB’s GLM Tool
Don't do this stuff by hand!! Especially if you have MINITAB.
Any crossed Gage R&R (as opposed to nested), no matter how many factors (typically parts, operators, repeated measurements) can be analyzed using MINITAB's General Linear Model tool. First I'll explain how to use it for a typical GR&R so you get the idea, then I'll mention the within part variation.
For a typical GR&R, think if it as a general factorial DOE with two factors - PARTS at 10 levels and OPERATORS at 3 levels.
Create columns as you normally would, with each measurement on a unique row, a column to identify the part, a column to identify the operator, a column that contains the measurement, and optionally a column that contains the repeat number (not really used in the analysis).
Open the MINITAB General Linear Model tool under the ANOVA menu. Enter the MEASURE variable into the Responses field. Enter the PART , OPERATOR, and PART*OPERATOR variables into the Model field. The later item is the part*operator interaction, which you really should look at. Enter the PART and OPERATOR variables AGAIN in the Random Factors field – don’t enter the interaction term there. This tells MINITAB that you want to analyze the variation between parts & the variation between operators (unlike the typical DOE).
IMPORTANT! - Make sure you select the Results button and check the Display expected mean squares and variance components checkbox. This makes MINITAB output the variance estimates for Parts, Operators, and Repeatability – which is just what you want.
Now, look in the session window for the variance estimates. They’ll be in the table called Variance Components. We’re almost there.
Now, just to clarify, the row labeled Error represents the Repeatability, the rows that contain the label Operator combine to represent the Reproducibility, and all the rows that except the one that says Part combine to represent the combined Gage R&R. This next part is easiest to do in Excel. To build the VarComp column that is found in the MINITAB GR&R:
Variance Source = Variance Component
(upper case terms refer to the values in the Variance Component table)
Total Gage R&R = OPERATOR + OPERATOR*PART + ERROR
Repeatability = ERROR
Reproducibility = OPERATOR + OPERATOR*PART
Operator = OPERATOR
Operator*Part = OPERATOR*PART
Part-to-Part = PART
Total Variation = PART + OPERATOR + OPERATOR*PART + ERROR
Now just divide each of these row Variances values by the Total Variation value to calculate the %Contribution column.
Now create the StdDev column by taking the square root of the respective variances.
Now multiply each of the StdDev values by 5.15 to create the StudyVar column.
Now divide each of the StdDev values by the Total Variation StdDev value to create the respective %Study Var.
You’re done. You can create the main effect and interaction plots typically provided in the GR&R output by using the Stat > ANOVA > Main Effects Plot and Interactions Plot tools. For the Interactions Plot I’d suggest you enter OPERATOR before PART in the Factors field, just to be the look you expect.
Now, about the Within Part Variation. This is done the exact same way. Make sure you measure each part several times (repeatability) in several standard locations (the within part variation – I’ll call this data’s column LOCATION). Enter the data into the General Linear Model dialog box as follows:
Response: MEASUREMENT
Model: PART OPERATOR LOCATION PART*OPERATOR PART*LOCATION OPERATOR*LOCATION
Random factors: PART OPERATOR LOCATION
The Model field tells MINITAB to include not only the main effects, but also all of the possible interactions, which should be looked at. If these are insignificant (the respective ANOVA table’s p-values are less than 0.05) then they can be left out of the model. Don’t forget to check the Variance Components option in the Results dialog box.
Now you’re ready to start combining variance components. Any variance component that contains the OPERATOR term is considered part of Reproducibility, and thus also part of the Total Gage R&R. The LOCATION and PART*LOCATION terms aren’t part of the Total Gage R&R – they are characteristics of the stuff being measured – more akin to part-to-part variation So the table might look like this:
Total Gage R&R
-Repeatability (the Error variance component)
-Reproducibility (the sum of all terms containing Operator – or any other measurement error sources)
--Operator
--Operator*Part
--Operator*Location
Part
Location
Location*Part
Total (the sum of all the variance components
Get the relative percentages (% Contribution), take the square roots to get the StdDev, calculate the 5.15*StdDev’s, and divide the StdDev’s by the Total StdDev to get the %Study Variations. You’re done.
You can create the respective main effect and interaction plots using the same technique.
Now that was easy wasn’t it? You can use the same general method to analyze any measurement system with just about any source of variation (multiple test bays, multiple test heads, etc)
