Does any know how much power the alarm going off drains? A few kitchen issues, humidity from the shower, grumpy toaster..... How long is the battery life if the unit is doing more than just waiting?
There's no way to know for your specific smoke detector.
Every six months, I break out the pulse-load battery tester (the one I like is
http://www.batteryjunction.com/zts-mbt.html, no affiliation) and test the Energizer Lithium AAAs in my smoke detectors. If they don't all test at the same level, I replace them. If they test out at less than 60%, I replace them. Given that a smoke detector is good for ten years max, I end up replacing the batteries approximately twice before replacing the smoke detectors.
With alkalines my advice is to replace them every six months without bothering to test.
Most battery testers are just voltmeters, and don't test the batteries under load. In other words, most battery testers are next to useless.
If you have any doubt, replace the batteries.