Time series intervention analysis

Let’s say I have a time series of store sales for a store. I have specific times where an intervention occurred, for example a store inspection. Each intervention is done by a coach using a specific questionnaire (for example food safety). How could I quantify the effect of the interventions on the store sales after an intervention, also quantify the effect of each coach and how long the effect usually stay there if there is one?

I am thinking a hierarchical model, where stores, coachs and questionnaires each share some priors, but not sure where to start.

Thank you!

I would take the time points after intervention, subtract with the average sales before the intervention (treated as baseline), which should give you a decay time series. And then I would start with a linear mixed model, with coachs as fixed effect, stores and questionnaires as random effect. Then from the intercept you get the effect of each coach, and from the slope you get how long the effect usually stay there if there is one.