if youll re-read my post, i think i already answered your question, but maybe i wasnt very clear. you will make steady progress upward, without failure, for a number of weeks. you will hit a point where the steady progress isnt so steady any more. maybe it takes you 2-3 weeks to get all your reps with a new weight. you will eventually hit a point where progress stops. when this happens, you will change something, and start your new rep/set scheme at a lower level, assuring that you get all your reps for several weeks as you slowly ramp back up. and the process will repeat.
now, when done correctly, this is largely self regulating. thats why it works so consistently. it you follow the rules, its hard to screw up. when you get to really hard weights doing a certain thing, it is certainly more stressfull than during the first couple of weeks you did it... this extra stress each week spurs the body to adapt. at some point, most often when you have been doing the same exercise and rep/set scheme for a month or two, and are not getting all your reps week after week (in other words, going to failure) the body just wont adapt to it anymore. so you make a change, and after this change, for a time, the workouts arent as stressfull, but still they are increasing each week and eventually youll be going full out again, and eventually you will go to failure again, and at first this will spur progress, then progress will stop, and it will be time to start over again.
so, typically, a person might NOT get to failure for 3-4 weeks, then might have a week where the workout with the specified weight was not completed successfully (in other words, FAILURE) then maybe the next week you are successfull with all your reps (NO failure) then, because you were successfull, you up the weight by a small amount again, and this time, you go two weeks in a row without hitting all your reps, and actually dont improve... SO, you make a change, maybe your change is that you were doing 3 sets of 5 for your work sets, and you change to 5 sets of 5, or you change to 2 sets of 10, or you change to 3 sets of 3, whatever, it doesnt really matter for this discussion, but when you make that change, you use your head and start on the first week with a weight that is conservative, and you then again arent going near failure, but you again add weight each week, and repeat the process. so thats 4 weeks without failure, then one week with failure, then one week without failure, then two weeks with failure, then back to 4 weeks without failure.... etc.
thats about as clear as i can make it. but one other thing... you are NEVER trying to go to failure. you are ALWAYS trying to make all your reps. failure is just that, a FAILURE to complete your workout. if this happens a couple of times in a row, you change the workout.