How do you know you're ready to add weight?
For most people it's easy: do you feel confident that you can REALLY step up the weight next session and hit your target reps with good form and technique without hurting yourself?
If yes, add the weight. If not, hold or back off as explained above.
As long as your sets feel hard, like you're trying to lift it with most of what you have, and you still met your target reps without using momentum or putting your body in risky positions, then that's the first signal.
There's really not that much science behind it.
Just beware of hitting failure before you hit your targets. Miss your reps because the set ran out on you, and that's your signal to back off.
You don't need failure to grow, either. Sets stopped a rep or two short build about as much muscle as sets taken to failure, and failure adds 24 to 48 hours to your recovery. Stop with one or two reps left and you keep the growth without paying for it in recovery.
With APEX we make it a bit easier. We tell you to rate each set on how hard it felt and how close to failure you were, or how much you had left in you. You just rate accordingly, then the formula decides.