This sounds a lot like wurm. I’m not sure what wurm uses for its calculates for item results, but here is just some idle guessing/chatter:
Quality should depend on these factors:
- The quality of your components (average them all)
- The quality of your tool
- Your skill in that area
Find the one with the least value. That is the lowest possible quality result.
Average the three. That is the highest possible quality result.
The result is a random number, from the least possible value to the highest possible value.
Producing raw materials from ore or trees is a special case, you only have 2 numbers to average instead of 3. Let’s say you have just started the game. Your chopping skill is 1. You have a 10 QL axe.
The lowest value is 1 (your skill).
Average 1 (your skill) and the axe ql (10). The result is 5.5. That is the highest possible value.
So now, the QL you assign to the tree you chop down is a random number between 1, and 5.5. Let’s say you assign it a 4.
Ok, so let’s say you want to chop a log from the fallen tree.
Take the quality of your components and average them. You only have 1 component (the tree), it has a QL of 4.
The quality of your tool is 10.
Let’s say chopping down that tree gave you a skill point, and your skill is now 2. This obviously isn’t wurm lol. Anyway…
The lowest possible value is 2.
The highest possible value is the average of the three, or 10+4+2 = 16/3 = 5.3333.
That sucks…the highest possible value is a little lower than 5.5…but the lowest value is higher. Plus…we only had to average 2 things before, from now on we use an average of three. Remember, only items created from raw materials (standing trees, ore veins) average with 2 items.
So you will at least produce a log from the tree of QL 2 instead of maybe 1. Yes, the max possible QL is a -little- lower…but not much.
If you just chopped down another tree, you would produce a possible fallen tree with a QL that ranged from 2 (not 1 this time) to 10 (your axe QL). That means a possible QL from 2 to 6, instead of 1 to 5.5 for your first tree.
And so on it goes. You slowly produce better items.
I don’t recall if wurm limits the maximum QL of an item you craft to the average of its components, though. Like…if you have a skill of 100, and a tool of 100, can you produce a 66 QL board from a 1 QL log. Seems like that would be impossible…so maybe the math needs to be worked on 
Anyway…this is just ramble. It may break down in some cases, I haven’t planned this all out in depth (yet) 
Hope that is of some interest to you, and use.
By the way…I would advise you store player skill as a float. You may just display it as an int…but with this system, every point counts.
When players are all the way up at skill 90…if it takes three months to get to skill 91, you darn well might want to show their progress all the way down to the thousandths! It could be a huge psychological factor for them. At -least- they could see some progress!