The computer is a Studio XPS. When I bought it some 3-1/2 years ago it was Dell's top of the line desktop. I plugged in into my existing UPS and did a test and the computer shut off. After some research this is what Dell told me, and I had to buy this higher-cost UPS to work with it. Of course you may be right, perhaps it's just a quirk of a poorly designed or cheap power supply and Dell was blowing smoke. Fact is, however, the system has been working without a single glitch for all this time.
My RAID is a Burly 2-bay unit with a host card from Mac Gurus - pretty bare bones setup.
Anyway, I decided to use a low tech approach to my problem - I moved the RAID box to where the power light is visible!