A simple tester, that in association with an oscilloscope in X - Y mode, can produce "signatures" for a number of different components. You can test in situ, and compare the signature with that of a known good component.
As with any devices connected to Mains Electricity, you must take extreme care in construction and wiring.
Here are some signature traces:-
Click here for a pdf file (530k) containing additional information on testing FETs.
G4WIF has a commercial version of this called the "Huntron Tracker".
I wondered why it was called the "Octopus tester" and Richard provided an explaination :-
Its called that because if you use a signal generator for a signal source (it does not have to be the mains and a transformer) you have cables running in lots of different directions, hence the name Octopus. I had used a signal generator for years until I decided to incorporate a transformer and not the separate generator. - de Richard W4MCD