Gage RR

This one is pretty simple…..Just do a simple paired t-test comparing the differences between the two gages and zero, the ideal difference if both gages & measuring processes were exactly the same.  A paired t-test is nothing but a 1 sample t-test using the differences between the two gage reading for each part rather than the individual part readings. I hope this helps.  Look at the confidence intervals to determine what differences you need to see for a 75% change.  Good luck!

What is this gage? does it measure attribute or variable characterisitic?
This is what I think can be done, I am not sure, but do an MSA for both the gages the reduction in %R&R value will give you the comparison for both gages. Select more than 20 samples if you are doing MSA on attribute characteristic.

Both DrSeuss (paried t-test and null hyp. as stated) and Jack (expression ) comments are extermely and valid useful. 
I would like to add this comment with a real LSL and USL values.
Say,  USL = 9.8 and Target of = 7.8 and LSL can be determine, using Jack expression – I would rewrite it in this fashion :
LSL = USL   –   2 (USL – Target)
The way Jack expression is written may look like value 2 is to the power, if this valid then LSL = 7.5, I would disagree with that. But in fact it is multipling the content of the bracket with 2.  If this have cause some confusion!
Therefore,
LSL = 9.8 – 2(9.8 – 7.5) = 5.2
This is right, USL and LSL specification limit of our product 9.8 and 5.2, where we target, 7.8. But due to the process varation, sample mean (target is between 7 and 8).
Hope this worked example and comments, are useful. If you need any further help, post your email, will respond, significant experience in Gage RR and paried T-test vs specification development and customer and supplier specifcation reviews. 
 
 
 
 
 

RogueBB,
If you have a lot of parts that you can measure, could you try the following?
Take 60 parts from one, homogenous (as best as you can tell) population.
Randomly divide the 60 into 2 groups of 30.
Measure first group with old gage, then second group with new gage.
Calculate variance of each group.
Total Variance = Variance of parts + Variance of gage, so assuming parts came from same population, the difference between variance of group 1 and variance of group 2 is the improvement in your gage.  Take the square root of the difference of the two variances, and that should theoretically be the reduction in your sigma from the old gage to the new one.  Since you have Total R and R numbers from the old system, I assume you can get the sigma of the old gage.  Divide the sigma you calculated above (square root of difference of two variances) by the sigma of the old system, multiply by 100, and that should give you % improvement (actually percent reduction of measurement variability) from old process to new process.
The above sounds crazy even to me, but it may be valid.  I look forward to hearing your comments.

Yes you can do a paired T test for MSA but I am not sure how can measure twice on a same sample if your test is destructive (I believe this is what you meant when you said that you cannot run the test twice on the same gage.). Otherwise paired T test can be used, only constraint which I see is that be sure that your data is normal atleast to some (p=0.03 or greater) extent. I hope this helps.
hemanth

We used to use the paired t test before we found the GR&R stuff. The basic issue is as the name suggests (pair) that it allows you to compare 2 things. If you have more than two readings for repeatability , there is a problem. If you have more than 2 operators (reproducibility) there is also a problem. That is one of the advantages to ANOVA.