Analysis of this action would be a fairly simple task taking only a few hours to a few days by someone familiar with the process. The analysis can tell you the stress at the weak points. If any issues are found it is simple to add metal or eliminate stress concentrating features. If it is found the weakest points are 4 or 5 times stronger than they need to be there is not much left but normal testing.
Proof testing is done even on very strong designs just to insure that hidden defects due to material flaws or workmanship do not get into the finished product.
More testing depends on what customer might want or expect or what the designer deems adequate.
I worked for a military contractor with its own testing facility. Very little that we did would be applicable to a consumer quality firearm other than life cycle testing.
All the so called lab testing kicked around in previous posts is not very relevant.
Some of that testing is:
1. Resistance to humidity and corrosion
2. Vibration testing in multiple axes
3. Shock testing in 3 axes
4. Centrifuge tests
Many of the tests are totally irrelevant because there is no reasonable requirement. You might test the loudness of operation for a military weapon. For your home built single shot who cares?
What you might care about is simple life testing.
You might be happy with 200 to 500 rounds fired in normal range shooting.
You might be happy wit 100 round for a deer rifle.
If you are building a prairie dog rifle more life cycle rounds might make you happy.
This does not have to be a formal process. You can just use the rifle and keep an eye on its condition.