I have a customer reporting this problem as well. Out of 20 or so parts he cuts on a waterjet machine, two parts would be almost 1/8" out of spec. He has seen this several times.
Another aspect of this was rapid moves being way off the spec. The computer screen shows no issues but the cutting head is noticeably not where it's supposed to be. While on a visit there, I also saw this problem The X axis on the machine moved over two inches further than the program called for on a rapid move. This particular move was toward the machine zero. This was about 10 minutes into a 12 minute job.
Any ideas?