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If you don’t know what exact items will be in the chest this won’t work as you have to program each combinator individually.
However, that won't actually do what you want. The problem is that different items have different stack sizes - e.g. 100 iron plates take up 1 slot, 100 steam engines take up 10 slots, 100 artillery shells take up 100 slots. To find out the number of used slots, you need to take the inputs, divide them by the stack size (using one combinator per item), round up, and then add them all together.
Without a pairwise combinator (multiply each signal on the green wire by the matching signal on the red wire), I can't see a way of doing this in a way that wouldn't require comically massive combinator arrays.
Also you can use inserter connected to the chest to disable loading at a certain capacity instead of alarming.
Sorry if this doesnt apply
https://steamcommunity.com/sharedfiles/filedetails/?id=1386495690
Is that what you meant or is there a more efficient way to filter signals?
But like I said this was just what I thought of right away. There may be a much better way.
Being lazy, I went for a far simpler solution and came up with this proof of concept:
https://steamcommunity.com/sharedfiles/filedetails/?id=1386569930
The idea is that once the storage chests start to fill up, the belt will also fill up. The combinator simply counts the amount of items on the belt and the speaker will inform the player once a certain threshold is reached.
It's very basic but at least you don't have to adjust any stack sizes ;)