One of my pet peeves is when people say that a point outside the control limits is a special cause. It is not. It is an indication that it likely a special cause exists, and that special cause thinking is the correct strategy to use to seek improvement. But that doesn’t mean there definitely was a special cause – it could be a false signal.
Similarly, a result that doesn’t signal a special cause (inside the control limits without raising some other flag, say a run of continually increasing points) does not mean a special cause is not present.
The reason control charts are useful is to help us maximize our effectiveness. We are biased toward using special cause thinking when it is not the most effective approach. So the control chart is a good way to keep us focused on common cause thinking for improvement. It is also very useful in flagging when it is time to immediately start using special cause thinking (since timing is key to effective special cause thinking).
However, if there is result that is close to the control limit (but inside – so no special cause is indicated) and the person that works on the process everyday thinks, I noticed x (some special cause) earlier, they should not just ignore that. It very well could be a special cause that, because of other common cause variation, resulted in a data point that didn’t quite reach the special cause signal. Where the dot happened to land (just above or just below the control limit – does not determine if a special cause existed).
The signal is just to help us systemically make the best choice of common cause or special cause thinking. The signal does not define whether a special cause (an assignable cause) exists of not. The control chart tool helps guide us to use the correct type of improvement strategy (common cause or special cause). But it is just a signaling device, it isn’t some arbiter of whether a special cause actually exists.