Useful
Correct Aterpster, you would want Alert Height to be as high as possible, it is a measure of aircraft capability.
On the other hand, of course, you want Decision Height to be as low as possible.
Reading the posts, it seems a lot of people do not fully grasp the meanings of AH and DH.
If you make an autocoupled ILS approach with a fully serviceable aircraft, on many Boeings that will give an Autoland Status of LAND 3, then your Alert Height is 200 ft. If, below Alert Height, an engine fails, or a generator, or whatever SINGLE FAILURE, then, technically, you can let the aircraft continue it's autoland.
The status of the ILS or weather has not been mentioned yet, in this paragraph. If it is CAVOK and the ILS is only Cat 1, no Low Vis procedures in progress, then you can still let the aircraft do its trick, provided you have had enough visual reference before descent below Decision Altitude. If LowVis procedures are in force, with a DH, you must have ample visual reference before DH, but that decision is a different one than the decision to continue after a single failure below AH.