Simple anomaly detection for metrics with a weekly pattern

I'm wondering if there is added value in replacing the proposed simple alarm function with control charts: https://en.wikipedia.org/wiki/Control_chart

The criticisms leveled against control charts in the wiki again elucidate a common problem with the state of statistics today. If experts, who have thought long and hard about the philosophical implications of likelihood versus significance, cannot reach any consensus, then how do we teach experimenters or engineers to correctly apply practical statistical tests or draw the right kind of inferences?

In Six Sigma we track stability using what is known as "The 7 Run Rule" [1]

Not only do you want to see spikes but also unusual activity that suggests further investigation is warranted.

[1] https://www.qimacros.com/control-chart/stability-analysis-co...

I'm looking to use machine learning somehow to get a baseline of weekly listener activity of the scanner feeds on broadcastify in order to spot anomalies of potential newsworthy events. This is motivation that what I have in mind is doable.