There was a vessel detention by AMSA recently becoz the cooling water for the RB engine was not functional. The vessel's critical list showed it carried a spare part for the cooling water parts, but was not traced on board. 

Obligation to carry spare parts for critical equipments onboard is mentioned in the company SMS. It is upto the vessel's staff to identify which equipments are critical ( Critical meaning those equipments which are part of the vessel's statutory certificates) and ensure that the spare parts are available at all times. Incase the company does not supply, then make sure it is in writing so that your part is clear incase asked by any Port State.