For precision machining, and its associated non-normal uniform distribution (which has no dependence on the mean whatsoever and the standard deviation has little to offer), you can not
predict a minimum number. It depends on the tool wear rate, and how many parts is takes to generate at least one cycle of the sawtooth curve (unless you are willing to extrapolate based on the tool wear rate determined from a sample) For example, if it takes a week and 3000 parts for the tool to wear from the lower control limit to the upper control limit, then 3000 is the minimum - but if it takes 5 parts to wear at that rate, 25 parts will give you 5 cycles - or more than enough data. A little simplistic, but should illustrate the point effectively. It is critical to collect the data in time order to evaluate the tool wear rate. It is not a random sample function, as the tool wear rate is a dependent (not independent) function of time. As a dependent function, CLT does not apply, either.
Again, the previous link gives some direction to this issue.