I am assuming you are discussing HTTP type monitors. I haven't tested this since 10.x. But I will assume 11.x is the same. For interval/timeout, it appears the LTM does something every interval no matter if the health check passes or fails. Here are some notes I took when testing. For failure testing, I just ran netcat on my server to listen but not respond to any HTTP queries.
The interval takes effect whenever an HTTP health monitor connects to the pool member. This behavior is different if the health monitor passes or fails. For a passing monitor, the successful GET will close the connection and mark the pool member up. The LTM will then use the interval timer to establish a new connection. For the default interval/timeout 5/16, the health monitor may invoke a new connection and GET around every 5 seconds.
For a failed monitor, the LTM will establish a connection to the pool member and send up to 4 GET's, per the interval set, before closing the connection. If, after 4 GET's, the timeout has not been met, the LTM will establish a new connection and will continue this behavior until the timeout has been exceeded. At that time the LTM will mark a pool member down.
Hope this helps