Ah, right. So use the family table to set a component parameter that shows up on the level above? Straight up that's not possible, as far as I know, since component parameters aren't owned by the individual part (that's their whole point!), but rather by the assembly itself.
You could do it with relations setting the component parameter of an instance to equal the part parameter of that part, but it would have to be specific for each assembly, as you have to identify which components it should apply to.
You could probably automate it, for example looking for all instances of a specific type of part and setting its component parameters, but that would require scripting, like the VB API, or WebLink, or JLink, or something similar.
