Total Measurement system error calculation

You need to do a precision and accuracy study.  You can find many topics on this site.  Let the data speak for itself but I have never a pH probe give a total variation of only +/- 0.01. 
Don’t forget to include the person using the probe since I’m assuming this is not an in-line system.  People can have an impact on pH readings.
Good luck.

Initially, I would prep for a simple gage R&R using sample solutions  prepped in numbered beakers.  Prep samples ranging from the lowest to highest pH for which you use the system (but not really caring at all what the true pH is for each sample).  Then perform repeated measurements in random order and compare the variation of indicated values within each sample.  The issue could be cross-contamination by the probe, but use your standard probe cleaning method and you will be capturing your systems true measurement variation.