I don't have experience on operating CNC machine but I do incline to bobdoering's lines of thought in the topic.
More than often in my real world experience, the focus has been shifted from understanding the process to the no-brain application of Cpk. It is always easier to push all this work to the supplier !
In my company, we also have active manual intervention on grinding process to compensate for tool wear. But the process behavior was studied before setting up the method of intervention.