How to detect if the process is in control

How can I detect if the process is in control?
By the control charts? If so, do I admit that whenever there is a special cause acting the process is out of control? Or in other words, if there is one point outside the control limits in 1000 points, do I admit that it is out of control? In other words, how many special points/causes are there that make the process out of control?

Would like to know your opinion. Thanks

This will probably stir up an argument from purists, but I will give my take on it.

Entropy drives things into a state of disorder. The state of being in-control is an unnatural state. That is why there is an entire industry established to manufacture and sell industrial controls. Left on their own, all processes will eventually go out-of-control, so control is a positive action taken to correct a process as it begins to go out of control. Some processes will deviate faster than other processes. A process can be controlled in one of two ways 1) use of an automated industrial controller, or 2) manually through SPC where you must take measurements, assess whether the process is still in a state of control then act to correct when needed.

As long as you are measuring the process at a reasonable frequency, and acting immediately to correct the process, when necessary, the process is in a state of control. If you have an excessively long frequency or delay acting to correct the process, then the process is out-of-control.

I used to work in rubber extrusion many years ago. Batch to batch variation was high, so we would take our samples after each batch change and immediately adjust the process as necessary thus controlling the process. Basing your judgment on what percentage of points are outside the limits is falling into the error of probabilistic thinking about SPC.

There is nothing wrong with process adjustments as long as you aren’t chasing random variation. That just increases the overall variation. Miner’s example is not chasing random variation…

As to the OP’s question:
A process that is in control will have between ~3% to .3% of the subgroups beyond the 3 sigma limits. This is NOT a signal that the process is out of control it is a signal that the process is in control. But there are very few processes that remain in control for 1000 subgroups. Nor would anyone want to wait for 1000 subgroups to assess the state of control or to detect an out f control condition. This is not an opinion but a demonstrated fact.

A special cause (or more accurately an assignable cause) is present when 1 subgroup is beyond the 3sigma limits, 2 out of 3 sequential points are near the 3 sigma limits, etc. see the Western Electric rules or the Nelson rules for more…Note too that this assumes rational subgroups.

From your first couple of questions I think you may not have researched SPC very deeply. It’s really great that you’re coming here to ask very good questions, but at this rate it will take forever for you to get to where you want to be from a knowledge standpoint. I strongly suggest that you begin reading the works of Donald Wheeler (go to SPCPress.com to begin - his articles are free). I posted links to many of them on your other thread.