I capacitor will also have a percentage rate printed next to the uf number, would look something like this on your 15uf:
15uf +/- 10%
What that means is this particular cap is good for that motor for up to 1.5 above 15uf (16.5) to 1.5 below 15 (13.5uf), taking 10% of 15 and adding or subtracting from it to achieve that number range. Your actual cap may only be plus or minus 5%, not 10. The percentage rates vary per cap.
Most condenser fan motor capacitors are not going to be above 10% of the uf number. Change that cap, it's too weak to start that motor.