The basic idea here is that the parts themselves have variation that must be measured. This within part variation would normally be incorrectly added to the repeatability, but if measured, can then be removed from the R&R.
The formula you refer to comes from standard nested design analysis methods. I might suggest you look at Douglas Montgomery’s “Design and Analysis of Experiments”, Chapter 13.
An interesting note: I took the data from Figure 16 in the AIAG MSA manual and ran it using the ANOVA method (using MINITAB’s GLM tool with the variance component output and then generating the % Contribution and % Study Variation values using an Excel table). I got very different results from those listed in Figure 17. Here I’m giving you the values from Figure 17 and the % Study Variation counterparts when using MINITAB GLM’s variance components.
Source = Fig 17 Value / ANOVA Value%EV = 4.2% / 13.8%%AV = 15.3% / 13.6%%R&R = 15.9% / 19.4%%PV = 97% / 90.8%%WIV = 18.7% / 37.0%
I know the math in Figure 16 includes lots of rounding, but always hate to blame such large differences on “rounding errors”.
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