Gauge verification with production data

Is it possible to use production data to see if the measurement equipment is measuring correctly? My company has several machines that make small round parts. Typically the diameter of the parts is within a normal distribution. So if I use hypothesis testing for mean and I see the mean of the production data is changing could that be an indication that the measurements are drifting? Therefore there is something wrong with the measurement equipment? For this to work how would I set this up? Could I compare historical data on a given manufacturing machine to new data from the same machine (Z-test)?

 

To your questions:
Is it possible to use production data to see if the measurement equipment is measuring correctly? - NO. You don't know how much variation is caused by the process or by your measurement equipment.
So if I use hypothesis testing for mean and I see the mean of the production data is changing could that be an indication that the measurements are drifting? - it could be the indication that the gauge is drifting. But also not. Read my first answer.
Could I compare historical data on a given manufacturing machine to new data from the same machine (Z-test)? Yes, you could. But not to find out, whether your gauge works as it should be.

The only way, how to find out, how many variation comes from your measurement equipment(s) is to perform a MSA.
1. a Type 1 gage Study - bias and repeatability
2. a Type 2 gage Study (Gage R&R) - Repeatability and Reproducibility