A lot of this is the context... You're not trying to prove something is mathematically perfect. You're trying to figure out if the variation is common cause [0] or a special cause. It's ok if you get this wrong from time to time because it's decision support, and it's better to act on imperfect information than to wait too long for perfection.
[0] https://en.wikipedia.org/wiki/Common_cause_and_special_cause... Common causes are addressed by fixing the system as a whole, while special causes are addressed by fixing one-offs. For example if you are addressing variations in delivery times, you address small delivery variance by improving the maps, which help every delivery. You address the one-off variation by firing the guy who takes 3 hour lunches mid-delivery every few weeks.
[0] https://en.wikipedia.org/wiki/Common_cause_and_special_cause... Common causes are addressed by fixing the system as a whole, while special causes are addressed by fixing one-offs. For example if you are addressing variations in delivery times, you address small delivery variance by improving the maps, which help every delivery. You address the one-off variation by firing the guy who takes 3 hour lunches mid-delivery every few weeks.