Protect signal from noise in Arduino
You do not send a "signal" to relay as information that can get corrupted by noise from power lines. Your relay works because of a coil of wire, that becomes a temporary magnet when current flows through it, switching the circuit contacts.

Read here: http://www.circuitstoday.com/working-of-relays

Noise will not disturb switching the relay. 

I hope you are using a transistor to drive the relay, not directly trying to drive it form Arduino. In that case all relays that require more power than a GPIO of Arduino can deliver, will fail. Also, use a flyback diode in your circuit.