To check if the ADXL001 is functioning normally, you can read the offset (or
output) without enabling self-test and it should be within the datasheet limits
(at 5V supply: 2.00V to 3.00V; at 3.3V supply 1.35V to 1.95V). The self-test
checks the sensitivity of the accelerometer. Once you have an accurate initial
offset reading (you can even average 100 samples) then you can turn-on
self-test and the output should change by 217mV for ADXL001-500 at 5V supply as
specified in the datasheet, see attached snippet. These two checks are good
verification that the part is functioning normally.
These values will change if you use a different supply voltage.