Like J5 said above max out at most, once a month. I personally never max out unless its 8 weeks before a big competition, and I mean big because I dont have to take my A game to regular ones. But what you suggested is fine for trying to improve it. Lift the weight and if you get it take a 3 minute break. Use that time to focus or get yourself pumped up, although its for resting. Increase the weight as you see fit, normally I know my limits and boundarys so I increase 5-10 lbs max. Where as you dont you might see a 10lbs - 15 lbs increase efficient for you.
What Im trying to get across is on the day you do decide your going to max out an exercise, dont stop increasing the weight untill you can not anymore, dont wait to try again next week. Rest 3-5 minutes between tries and if you dont get a lift do not be scared to try again if you have a spotter, after you get your little rest in.