That would work. To cut the component count still further, you could remove the oscillator and the AND gate, drive an NPN transistor from the S-R flip-flop's Q output and have it switch a buzzer that beeps on and off automatically, something like this one:-
http://www.altronics.com.au/p/s6112-3-15v-pulsating-tone-piezo-chassis-mount-buzzer/
Something I noticed is that in this version, the alarm won't trigger if a sensor wire breaks or becomes disconnected.
You could also replace the OR gate with two diodes followed by a tie-down resistor.
And a single NPN transistor could replace the inverter.
Now the only IC would be the S-R flip-flop.
Thanks.Ran into a small logic issue.
1. What happens if an alarm happens, you hit the silence button, then another alarm happens before the first alarm input line returns to the safe state? My guess is that you want the alarm to go off again. This changes the set circuits. More later.
2. Also, in post #13 you said the inputs had 47K pull DOWNs and go low on alarm.
ak

OK, this probably is more like what you envision your circuit to be. It does not have the logical tightness of the previous post, but it covers the basics.
Note that there are two output stages. Either connect the high side of the alarms to the 555 and the low side to GND, or the low side to the FET and the high side to Vcc (and eliminate the 555).
ak
View attachment 21744
The posted image is a GIF, which any graphics program can handle. GIF files do not show compression artifacts the way JPGs do, especially with fine line drawings.
If you are committed to using the external switch to ground to complete the input LED indications, there is a circuit trick that gets you Red/Green indications with NO drivers. I'll post that later.
I think you misunderstood. Output option 2 pulses the beeper exactly the same as with a 555, but it uses the 4th NAND gate as the oscillator, saving the cost and complexity of another chip. Hysteretic gates have all kinds of fun inside.
ak
Well, call me old-school, but I just plain don't trust it to be as reliable as reliable as a normal piezo beeper, plus I don't like the higher profile..the one I have here is pretty flat.Wow, this thread's been busy. For some reason I've stopped getting alerts and email notifications for some of the threads I'm involved in, including this one.
This circuit is more what I was thinking of. Looks good.
Skidood, how come you don't want to use a self-pulsing buzzer/beeper? It would simplify things even more.