MSA for Calculated Clearance Dimension

#1
I have a situation where I have a shaft and a sleeve that are measured and the diametrical clearance between them is calculated as the difference between the shaft OD measurement and the sleeve ID measurement. Engineering has defined the diametrical clearance as a KC and is looking for the application of SPC and capability. There is a separate gage for measuring the shaft ID and a separate gage for measuring the sleeve ID. My questions is how would I approach the MSA study with two gages that contribute to error that affects the calculated diametrical clearance measurement. The requirement is that each gage have a P/T ratio less than or equal to 20 percent. Knowing that error is additive, I would expect that if each gage had a P/T ratio of 20 percent, the combined error would be more than 20 percent. Would anyone out there know how that combined error be calculated?
 
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#2
The variances (s^2) of the measurement errors are additive, but not the standard deviations (s).

Clearance variance (s^2) = Shaft measurement variance (s^2) + sleeve measurement variance (s^2); ignoring potential calculation errors

Once you determine the clearance measurement variance, you can calculate a P/T ratio for the clearance measurement.
 
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