I would suggest that you use a schmitt trigger input logic gate,preferably CMOS device ,possibly with some passive filter to suppress radio frequency interference.Arrange the input so that the NO-Alarm condition is high and Alarm condition is low as you have done,this is because the cmos logic gate has more immunity from noise in its logic high state than its logic low state,that means that when the signal is in its logic 1 state at 5 volts you can introduce more noise to the signal before the logic gate will see the 5 volts plus the noise voltage as a logic 0,than if you arrange it the other way round,Which is why things like memory chips have all their logic control functions as active low.
If you use a cmos device you can also run it at higher supply voltage and increase the trigger voltage from the sensor which will increase your noise immunity even more.
If you need a schematic I can send you one for the alarm circuit I have had working in my house for a few years with very few false alarms.
Jez