I just did 9 hydro test last Thursday, 4 of them were mine. Three of mine were steel 72 and per my calculations (a bit of a conservative REE calculated estimate) they all qualified for the + rating. And they were legally stamped with the + stamp.
It has been about 25 years since I operated a standard water jacket hydro test machine, but this is not rocket science. My LDS installed a hydro test machine a couple of years ago and I have help them with some technical advice and last Thursday I did a bunch of VIP and some hydros for them and got do mine for the right price.
SparticleBrain and James (fdog) are both partially correct. The test description from SparticleBrain is basically correct, but as mentioned in the CFR paragraph quoted by fdog, the water jacket method is the only acceptable method to perform the hydro test if the + rating is going to be added.
I am very familiar with the water jacket method and as far as I know it is the most common method for small cylinders. It is a very precise method and the initial equipment is probably much less expensive and easier to keep in calibration than the direct expansion method. I also have the impression that the direct expansion method may not be as precise, but I am not sure about that. I would think this is the reason the direct expansion method is not acceptable for the + stamping, but as I mentioned, I have never operated DOT approved direct expansion hydro test equipment. As an engineer I have performed similar hydro tests in a lab/ industrial environment and it was hard to keep any accuracy.
As Captain said, the direct expansion method is the only practical method for very large cylinders and in general it is probably much faster to perform a hydro test on any cylinder using this method. But, most small hydro facilities would probably not own the equipment for direct expansion hydro testing.
NorthWoodsDiver
The suggestion of adding your own + stamp next to the last hydro date is extremely irresponsible and bordering on ... (never mind... I don't want to sound insulting and I am kind of kidding). Now a day all authorized hydro facilities have licenses and are required to stamp them with the hydro date. It is very easy for an LDS to check if a + stamp is legitimate and I am aware of some that will and have done it. Granted, it will probably never be fully enforced, but falsifying federal code stamps is never a good idea, especially when it will not gain you much. If you read the code (CFR49) you will realize that an individual may own the tank, but you don't actually own the DOT stampings on a cylinder.
mattboy
The strength of the material of all 3AA cylinders is always the same by the code. As a matter of fact most use the same exact chrome-molybdenum steel alloy ASTM-4130. But material strength is only one of the three major variables in determining pressure cylinder allowable working pressure. The cylinder diameter and wall thickness are actually what determines the cylinder wall stress as the pressure is increased on a cylinder.
Hydro test pressure are design take the cylinder to the lower end of its yield strength. Due to manufacturing tolerances, I am sure may steel 72 could be tasted to 4000 psi and pass, but many would also fail. If you would like me to test your steel 72 to 4000 psi, I would be glad to...I have access to a hydro test facility. Granted, this would not be a DOT sanctioned test and no stamp could be associated with it. After the experiment it would be required to perform a conventional hydro test with the proper pass/ fail criteria since the tank would have experienced an unauthorized structural event.