In purchasing and procurement projects the sellers and vendors are first parties. The second parties are purchasers or buyers.
First party inspection refers to quality control activities that are done by equipment vendors or sellers.
Second party inspection refers to inspection activities that are done by equipment buyers or purchasers.
In fact first party is seller and second party is buyer. So when you say second party inspection, it means that an inspection and quality control activities that are done by a buyer and when you say first party inspection, it means that an inspection and quality check that are done by a vendor in its construction shop.

The Third Party Inspection refers to independent inspection activities that are done by a Third Party Inspection Agency either hired by a buyer or seller.
The ISO 1720; - Requirements for the operation of various types of bodies performing inspection- specifies characteristic of these kinds of inspection agencies.
Based on these requirements, these agencies must be impartial and independent in their inspection activities and in their inspection reports and results.
All interested companies such as traders, buyers, sellers, engineering companies, construction companies must have access to the services of these inspection agencies.