Factory on this island moving to start manufacturing minute parts (10)

'minute parts' is the definition.
(a millionth is a minute or tiny fraction)

'factory on this island moving to start manufacturing' is the wordplay.
'factory' becomes 'mill' (synonyms).
'this island' becomes 'i'.
'moving' indicates an anagram.
'to start manufacturing' becomes 'ths' (I can't explain this - if you can you should believe this answer much more).
'on'+'i'='oni'
'oni' is an anagram of 'ion'.
'mill'+'ion'+'ths'='MILLIONTHS'