OK, the scale has a horn that goes off when a "bad" bottle is on it. Down the line there is someone waiting to turn or step on an air valve to blow the empty bottle off the line about 16 seconds after they hear a horn?
Hopefully, this poor soul has some other job in addition to waiting for a horn and counting the seconds.
If I have described this correctly, then the person involved has two things to do:
1. Wait until the "bad" bottle is exactly in the right place to be blown off the conveyor,
2. Turn on the air for the correct length of time so that only the "bad" bottle gets tossed out, without toppling other good bottles.
If this is what you want, then you need:
(A) A sensor to determine when a bottle (any bottle) is exactly in front of the air jet.
(B) A way to know that this is the bad bottle,
(C) A timer to open, and then close a solenoid driven air valve after a set length of time.
A and C are off-the shelf stuff, you probably already know where to get them.
That leaves B, the waiting "about" 16 seconds part.
You *could* use a timer for that, started by the horn, which would wait 16 seconds (or a bit less),
then tell sensor A to start looking for the next bottle.
A better way would be to count bottles. You know that there are x number of bottles between the scale and the blower-person. Horn blows, (A) counts down until that many bottles have passed, then blows.
As far as designing this circuitry - YOU are the only one here who knows what voltages, amperages, environmental conditions (electrical noise, etc) are there to be worked with. Without those specifications, no real answer can be given.