Training volume is the amount of training a muscle gets over a period of time. It can be measured in many ways: as tonnage (weight × reps × sets), total reps or time under tension. For muscle growth, a simpler measure has won out: the number of hard sets per muscle group per week.
A systematic review by Baz-Valle et al. concluded that counting sets taken to or close to failure is a suitable way to measure volume for hypertrophy, as long as reps fall roughly between 6 and 20 or more.
What studies say about the dose
A meta-analysis by Schoenfeld, Ogborn and Krieger (2017) found a dose-response relationship: more weekly sets went along with more muscle growth, with the largest gains from about 10 sets per muscle per week. A larger analysis by Pelland et al. confirms the direction but shows diminishing returns: going from 4 to 8 sets brings more than going from 16 to 20.
That gives a working range of about 10 to 20 hard sets per muscle per week. Beginners often grow with less, and some advanced lifters tolerate more.
Counting compound lifts
On the bench press, chest, front delts and triceps all work. A proven approach is to count the main muscle fully and assisting muscles as half.
Example: 4 sets of bench press count as 4 sets for chest and 2 sets for triceps. This is a worked example.
More volume only helps as long as you recover from it. If performance drops over several sessions or your joints ache, less is often the better choice. Change volume in small steps of 1 to 2 sets, and only where a muscle has stalled.