Most of the power supply failure indicator circuits need a separate power supply for themselves. But the presented here needs no additional supply source. It employs an electrolytic capacitor to store adequate charge, to feed power to the which an alarm for a reasonable duration when the supply fails.
This circuit can be used as an alarm for power supplies in the range of 5V to 15V.
To calibrate the circuit, first connect the power supply (5 to 15V) then vary the potentiometer VR1 until the buzzer goes from on to off.
Whenever the supply fails, resistor R2 pulls the base of transistor low and saturates it, turning the buzzer ON.