Contact the engineer/surveyor from the company that is providing burst indemnity insurance at an early opportunity. Present the client with the insurance inspection test certificate following a witnessed hydraulic test with that individual in attendance.

My client wishes to understand how did I arrive at a weld deposit of 8mm for a transformer tank wall which is also 8mm in thickness.

Not to be a smart-alec, but how did you arrive at that weld thickness? Is it a single-pass butt weld? Pipes with higher pressures are usually welded in two or more passes with good (proper) penetration.

12 PSI ain't much, unless the volume is large and there's gas in the vessel, so weld strength is probably not much of a factor, but weld quality (integrity) is.

I suggest visiting Miller Electric's website. They have a welding forum and an industrial welding blog.