http://puu.sh/Fh42t/090d39afed.png
when you try to imput prod module in furnace from mod https://mods.factorio.com/mod/TheBigFurnace
it said you cant insert it here, while vanilla modules works and you should be able to do that.
i was be able to insert module few times (error didnt pop out) but module just did nothing at all
same with big circuit factory ( https://mods.factorio.com/mod/CircuitFactory )

It is a limitation of the mod https://mods.factorio.com/mod/TheBigFurnace
it don't allows tier 4 or higher productivity modules to be used

table.insert(data.raw["module"]["productivity-module"].limitation, "big-iron-plate")
table.insert(data.raw["module"]["productivity-module-2"].limitation, "big-iron-plate")
table.insert(data.raw["module"]["productivity-module-3"].limitation, "big-iron-plate")

table.insert(data.raw["module"]["productivity-module"].limitation, "big-copper-plate")
table.insert(data.raw["module"]["productivity-module-2"].limitation, "big-copper-plate")
table.insert(data.raw["module"]["productivity-module-3"].limitation, "big-copper-plate")

table.insert(data.raw["module"]["productivity-module"].limitation, "big-stone-brick")
table.insert(data.raw["module"]["productivity-module-2"].limitation, "big-stone-brick")
table.insert(data.raw["module"]["productivity-module-3"].limitation, "big-stone-brick")

table.insert(data.raw["module"]["productivity-module"].limitation, "big-steel-plate")
table.insert(data.raw["module"]["productivity-module-2"].limitation, "big-steel-plate")
table.insert(data.raw["module"]["productivity-module-3"].limitation, "big-steel-plate")

If you want you can just delite that part of the mod and it will work

i found that after posted this on furnace mod discussion, but when i tryed to change mod files, my game dosnt see mod anymore (im probably doing something wrong) but thanks for answering anyway

You have to unzip the folder then delite the Stuff
save youre change
delite the unchanged Zipfile and zip the new on
That shoud work

I have a question about a similar topic:
I wrote a patch for myself that changes a few little things of the Factorio Extended Plus mods.
I tried to allow the productivity modules for titanium and titanium alloy but I dont know how. I am not a modder.

In the recipes I added:

allow_productivity = true

and I tried to add a line like that for each module and recipe:

table.insert(data.raw["module"]["productivity-module-4"].limitation, "titanium-alloy")
table.insert(FactorioExtended["module"]["productivity-module-4"].limitation, "titanium-alloy")
table.insert(FactorioExtended["fb-module"]["productivity-module-4"].limitation, "titanium-alloy")
table.insert(data.raw["fb-module"]["productivity-module-4"].limitation, "titanium-alloy")

but non seems to work. Maybe you could help me out?
How do I access the limitation table of the new modules?

Basically, what I want to do is something like:

allow_productivity(recipe_name)

You can find more under
D:\SteamLibrary\steamapps\common\Factorio\data\base\prototypes\item module

¯_(ツ)_/¯

Thank you for your reply.

As far as I can tell I cant change the function productivity_module_limitation() in data\base\prototypes\item module without it being overwritten each new factorio update.
My problem is that I wrote a function:

function allow_productivity(recipe_name)
for _, prototype in pairs(data.raw["module"]) do
if prototype.limitation and string.find(prototype.name, "productivity", 1, true) then
table.insert(prototype.limitation, recipe_name)
end
end
end

allow_productivity("titanium-ore")
allow_productivity("titanium-alloy")

but it only allows productivity module 1, 2 and 3 for the recipes, but not for your productivity module 4, 5 and 6. How do I access the limitation table of your new modules?

I managed to fix the problem. Thanks.

One Question
Do you live in Europa