The research help says:
A star produces Y*(X+5) ships every 24 hours where X is your manufacturing tech level and Y is the amount of industry at a star.
This should be every cycle. A star produces
Industry * (Manufacturing + 5) ships every cycle. Cycles are 16 to 36 hours with default being 24.
Maybe the best way of wording it is something like:
Each Industry built on a star creates 5 ships per cycle. Each manufacturing level increases this by 1.
Then it’s easy to calculate how many ships a higher Manufacturing level will give you. It’s just equal to your empire’s industry.