There's a good rough-and ready check of pumping capacity. As
atmospheric pressure is
So you get a watch with a seconds hand and time how long it takes to
A calculation I did for my compressor is here. It's expressed in the computing language Lisp, which might mean you are best only seeing the general idea rather than looking for an example to copy.
Less exactly, if the compressor took a long time to come to cut-out pressure, that would indicate all was not well. A 3HP portable with a 50litre tank should take around two to three minutes to come to cut-out pressure.
By the way - a 3HP portable air compressor will not continuously keep up with the air demand of most air tools - so there is no basis for a test here.
Someone told me at a bus-stop once that there is a way to check the
valves of a compressor. It isn't something one could ever recommend
doing. If you take the air filter off a compressor and the run the
compressor, if you put your hand over the air inlet (!!!) you should
feel a constant suction on the palm of your hand. If any of the
valves are defective, you will feel an alternate sucking and slight
blowing. Now, this practice would definitely be forbidden. For a
start, on a good working compressor, it is going to more feel like
"something grabbed your hand". For two, you are going to have to pull
your hand off the compressor. The maximum force that can be exerted
(Richard Smith, June 2005)