roland_lu,
Here are a few thoughts that come to mind.
1) Could you reinforce the straps just for testing? Perhaps attach 2 or 3 straps to the same base so you could pull 2 or 3 times harder before the straps break? Or use thicker straps or straps of a different material?
Of course, if this affects the welds themselves, then the measurements of weld strength wouldn't be representative of the original welds and the study would be invalid.
2) There would be ways to work backwards from the failure data (or lack-of-failure data in this case) to get a bound on possible mean & st dev for the data
You know that 1200 have been tested and none have failed. Working backwards, it can be shown that if 99.75% of welds would pass the test, then there is just a 5% chance of not seeing any failures. If 99.62% of welds would pass the test, then there is just a 1% chance of not seeing any failures.
Or the other way around,
* you are 99% sure that at least 99.62% of the welds are stronger than the strap.
* you are 95% sure that at least 99.75% of the welds are stronger than the straps.
From there, it would be possible (making assumptions like a normal distribution which may not be especially accurate) to get a limit on the possible values of Cpk.
3) In the spirit of accelerated lifetime testing from reliability engineering, make a series of welds at intentionally poor settings. Perhaps you could do 30 parts at 70 % of the normal current and test those. Then do 30 parts at 80% of the normal current. Then do 30 parts at 90% of the normal current.
Then you could say something like
* at 70%, the weld had a strength of 100 +/- 20, which would give a Cpk of 0.5
* at 80%, the weld had a strength of 150 +/- 30, which would give a Cpk of 1.0
* at 90%, the weld had a strength of 250 +/- 30, which would give a Cpk of 2.2
We don't know the actual Cpk at 100% power, but it must be at least 2.2.
Just a few stray thoughts...
Tim F