The original intent of certificates of compliance was to make sure that process steps were not overlooked if they could not be verified later. An example of this might be a product that has to be dipped in a specified solution at a specified temperature for a specified period of time before painting or plating. Usually, there is no way to verify that these steps were taken once the product has been coated. Testing after-the-fact can reveal that the correct thickness of paint or plating has been applied but not that all specified process steps were followed.
Other than monitoring the entire process at the vendor, the only comfort the customer can get is through the use of a certificate of compliance.