I've explained it several times... The referenced thread is pretty good... In short the tonnage of a splitter is determined by the area of the PISTON in the cylinder, (not the rod) which may take a bit of guessing but is usually going to be an even inch or half inch value times the maximum working pressure of the pump - figure 3,000 psi unless you know it is something different. It has NOTHING to do with engine size, pump gpm, or fluid tank size, though these are important...
Thus tonnage = pi x R^2 x psi, where R is the RADIUS (or 1/2 the diameter) of the piston.
Pump size determines the cycle time in combination with the cylinder area and stroke length - area of piston x stroke length will give the volume of the cylinder, divide this into the pumps gpm rating to get the fraction of a minute to fill the cylinder, this will give the time of the down stroke. The up stroke will be a little less because the cylinder volume is reduced by the size of the rod, but doubling the down stroke will give a pretty good cycle time estimate.
MINIMUM Engine HP is a function of pump size - for the two stage pumps common on splitters, you need a minimum of 1/2hp per gpm of pump. For a single stage pump, you need 2hp per gpm. It is good to go a little over this on engine size, but going a lot over is mostly a waste.
Hydraulic tank volume is pretty much irrelevant as long as you have enough to fill the cylinder on the down stroke, and enough empty space to accomodate the extra volume on the up stroke, however a lack of volume can cause problems with overheating. The "book" on design theory suggests that most splitters should have about a 20 gallon tank to give enough cooling. Actual practice appears that most splitters seem to take around 5 gallons once the system is full of fluid...
Thus while all the parts are somewhat independent, upgrading is kind of touchy, and will rapidly get into a "chain reaction" that IMHO will result in you effectively buying a new splitter one peice at a time - my suggestion would be to upgrade by selling the innadequate unit and buying a new one, probably cost less in both time and money for most people...
Another upgrade consideration is the "under structure" - particularly the beam and attached bits like the base plate and cylinder mounts... Some machines it isn't an issue, the manufacturer uses the same "chassis" for several models and simply changes by putting different cylinders, pumps, and motors on. However if you have a small machine it was likely designed for the cylinder that was on it (will a larger one even fit?) and putting a higher power cylinder on may break things...
That said, ANY pump can be used to drive any cylinder, but a small pump on a big cylinder will give a very long cycle time, which most will rapidly find annoying. To get the typical ~15 second cycle time you essentially need an 11gpm pump on a 4" cylinder, or a 16gpm pump on a 5" cylinder.
So if you start trying to upgrade - you first step will be to put on a bigger cylinder... If the beam doesn't break, you will get a lot more splitting force, but your cycle time will seem eternal.
So you will want a bigger pump. However, that will probably also mean you need a bigger engine... At which point you will have replaced all the major parts, and probably spent close to as much as a new splitter the same size would have cost you....
However don't sell the little splitters completely short - we have a fair number of users that have them, and report that they can split most of what they throw at it, although they may need to use a bit more finesse to do so... I have a big 30 ton unit, but I can tell from watching the pressure guage I put on it that in practice, I could have split EVERY round I've used it on (including some 30-40" curly maple crotches) with 20 tons or less, mostly a lot less - it is a tough round that I need more than 1200 psi to break...
Gooserider