If you found a fuse that have problem be it in the main line or in the secondary side for example the pico fuse in the inverter board-don’t just direct replace the fuse and turn on the equipment. Chances is high the fuse may break again. Yes fuses sometimes have it own life span or broken when hit by a small surge and by replacing only the fuse will usually solve the problem.
As for me i will always check along the fuse line for any shorted components especially the semiconductor before putting a new fuse and turn the set “On” again. At least this will prevent from wasting another good fuse just incase if there is still problem with the board. Always scan through all the semiconductor components like IC, DIODE and TRANSISTOR. Sometimes a shorted capacitor (e-cap and non polar cap) may also cause the fuse to burn but the percentage is smaller as compare to a shorted semiconductor.
So don’t be happy if you found the fuse open circuit and you have to still troubleshoot to find out the cause of fuse blown. If everything checks to be okay then only you switch On the equipment.