This is probably not as common as tachycardia for anyone in a hospital.
The only healthy people with a resting pulse under 40 bpm are long distance runners. (probably less than 10 in the whole world with a resting pulse that low) and they would never be using the product anyway so you can eliminate that scenario.
professional cyclist Miguel Indurain had a resting heart rate of 28 BPM).[2] Martin Brady holds the world record for the slowest heartbeat in a healthy human, with a heart rate measured in 2005 of just 27 bpm.[3]
As the above link states, less than 40 bpm is absolute bradycardia
[A waking heart rate below 40 BPM is considered absolute bradycardia. ](http://A waking heart rate below 40 BPM is considered absolute bradycardia.)
I think you can use 40 bpm as your alarm threshold.