Some importers ask for a re-inspection but do not wonder what it implies in the factory. When a shipment is rejected, they simply tell their supplier to “repair the products and set a re-inspection date”. But this is not enough. If you are a buyer in this situation, what should you do?

First, ask yourself “can they really repair these issues?” If so, ask them to do it. If not, there are basically three options:

Let the supplier ship the goods as they are,
Ask the supplier to sort out the bad goods and either re-produce (if there is no minimum order quantity problem on the materials and if timing allows) or short-ship,
Ask the supplier to sort out the worst goods (according to an exceptional tolerance) and either re-produce or short-ship. (Note that this “exceptional” tolerance might well become the standard for future productions, in the factory’s mind).
Second, list the steps that should be followed by the manufacturer.

Hi
when the dealing is done through LC, and LC mandated for third party inspection, and the shipment is rejected by third party inspection but buyer says no problem and asks from third party inspection agency to issue certificate, then the inspection bodies ask a formal letter from buyer as" Letter of indemnity" then they might issue the certificate.

but normally this is not good practice and banker LC deportment forbids the inspection company to issue certificate with non conformance goods
for more detail review following articles in following site:

[www.inspection-for-industry.com]

Inspection and Test Plan
Shop Inspection
Preshipment Inspection

regards