Today i disassembled one cheap chinese light bulb. There are basically 3 component in it. A capacitor , a FULL BRIDGE RECTIFIAR , and 24-30 high efficiency LED's in series. Obvious one of this leds blow up , and the light bulb wont work. This circuit can be fixed adding a capacitor in the bridge rectifier output and place a 1W 1Kohm resistor in series to the 680nF capacitor.
http://s.aliexpress.com/Jf2YbIja