Product review (5 stars): Try This First Before Ordering
My Amana fridge starting to do a 15 second buzz followed by a click.  I cleaned the coils and fan, removed the relay to get a part number and put it all back together.  The buzzing was less frequent, but still there.  I ordered this part, and it fit fine, but it did not correct the problem.  The repairman said the compressor is almost dead (expected for the make of the compressor).

Before you order this relay ($40 in March 2014), you can do a few simple tests on the compressor first.  If you have an ohmmeter you can measure the resistance between the 3 pins on the compressor.  They should all be around 10 ohms or less.  You should also check for a short from any of the pins to the compressor's case.  There are some great youtube videos with more details.  I did this and my measurements matched what was expected.

If you have the equipment, you can also check how much current the fridge is drawing.  That is how the repairman checked ours; it was drawing 6 amps.  I don't have a cool clip-on ammeter like he does, but I could have used a Kill-A-Watt that I do have.  If I'd known how much current it was using I could have saved quite a bit of time, effort and expense by calling a repairman immediately.