When you start reading those articles from here on only (because someone did send you a direct link) without reading the first chapters, this will happen:
If so: Start from the beginning!
In this chapter, the 3 most commonly used quality control chart types are addressed.
There are other quality control charts available, but as these are rarely used in industry, they are ignored in this chapter.
A distinction is made by the strategy. At the beginning of the strategy are the tests for location and variation. If the process has no problems here, control charts for "single-peaked" distributions are used. This is classic theory and needs no further explanation here.
But now the exciting question: What do we do if the process and location and/or variation are not stable?
2 chart types are briefly explained here. The extended Shewhart chart and the acceptance chart. But when could which one be used?
Let's look at the process time models of type "C". These are stable in variation, only the location has a problem. Meaning: in each individual subgroup, the variation itself is the same. For these cases, an acceptance chart could be the right choice. This is because the acceptance chart is the only one that includes the specification limits. Roughly speaking, a safety zone is placed around the specification limits based on the internal variation (the variation within the subgroups).
This can ensure that you have enough distance from the limits, but "open" the control chart for production as much as possible if the position fluctuations are known.
In process models B and D, however, the variation is not constant. (and possibly not the location either. One possible decision here would be to start with the "extended Shewhart chart".
Means: First, a classic Shewhart chart is calculated:
However, the control limits are then widened by a factor that is calculated using the analysis of variance from the positional fluctuations of the individual values:
With the completely unstable processes, this could at least start with the QCC issue in order to gradually bring the process under control.
These are just suggestions. It is important to consider these with your own processes and decide whether they can be used as the first suggestion for saving a control chart.