Faulty Welding in Oil Coolers

I am going to take a WAG here -

How about testing your tubes and plugging the leaking ones?

(or describe your problem better)

That's a pretty thin tube sheet, unless the O.D. of the shell is quite small. A drawing would help, along with the fluids and temperatures involved.

I suggest you perform a failure analysis to determine whether the problem is material, process, or workmanship related. Visual examination of the leak site to determine if the leak is through a crack, a hole, or an incomplete weld, would be a good start. In parallel with your examination, determine when the problem began, and see if that time coincides with any change in materials or process.

i have often used silver to patch tube but is harder to find silver coinage this days