When you define an analysis to trigger based on any input, it will evaluate all new events from each input attribute against the last trigger time and only evaluate ones more current than the last trigger time(Order or execution).
Lal Babu Shaik
With event-triggered scheduling, evaluation occurs based on events. You can specify one or more input attributes that trigger an evaluation whenever the attribute value changes.
This means that if any of your 2 roll-up attributes update, the 3rd analysis will update as well since you set it as any input. There is also a choice to just select either one of them instead of both.
You can always examine the logs to see how things are evaluating, but if you have setup your analyses such that the output of one analysis is the input to another, the analysis evaluation should happen in a cascading fashion meaning the order of evaluation will look like analysis 1-> analysis 2-> analysis 3
This post talks about how to use the logs to determine the order of evaluation.
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PI Analysis Service will automatically group calculations that are dependent on one another. Additionally, dependent analyses are handled in a unique way-- the output data for each analysis is immediately passed to analyses further up the chain. This is all handled in process, and is designed to be abstracted from the user. Dependency chains help preserve data integrity throughout the chain by allowing the Service to calculate analyses in their intended order. This is also respected during backfilling/recalculation.
PI Analysis Service determines dependency based on two things: Analysis Template and Scheduling. Analysis 2 must use the output of Analysis 1 and must be the same schedule (Natural/Periodic).