But you need to know the process is 'in control' before establishing the control limits, regardless of the type of control chart. Knowing the distribution can help establish that. X-bar does help stabilize a non-normal distribution because the averages tend to be normally distributed, even if the individual distribution is not. (Central limit theorem)
If you had read the link to the past thread, you will find that whether or not the average tends to be normally distributed, in the tool wear scenario the average of the measurements of a sample of parts is meaningless. It will appear to be normally distributed because its primary variation will be measurement error from roundness or parallelism (not GR&R) - which is a normal distribution. But, that error is not what you are trying to control. In fact, in the process laid out in the link, you remove that error from your charting. Once you have removed it, you will find a uniform distribution. Any subset of a uniform distribution is a uniform distribution. "Central Limit Theory" does not apply.
You need to know something about the process before just putting a control chart on it, including whether or not the process is in control or stable.
Trend charts have been used successfully for tool wear.


