Inspection of German vehicle in the middle of factory (5)

I believe the answer is:

audit

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'inspection' is the definition.
(I've seen this before)

'german vehicle in the middle of factory' is the wordplay.
'german vehicle in' becomes 'audi' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'the middle of' indicates the central letters.
The middle letter of 'factory' is 't'.
'audi'+'t'='AUDIT'

'of' is the link.

Can you help me to learn more?

(Other definitions for audit that I've seen before include "Go over" , "special ale" , "Financial check" , "Financial investigation" , "Check of books" .)

I've seen this clue in The Irish Times.

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