So our current smoke detectors are going bad. They're hardwired w/o a battery backup. Replacing them with hardwired w/ battery backup. Theoretically speaking, if no power is lost, the batteries should last as long as the shelf life is, correct? Will the detector do any kind of self-check periodically to make sure the batteries are still good, and chirp if not? How long will the batteries last w/o power? The same as a 9v battery in a detector that was never hardwired?