Excellent question.
I'd love to go into detail to paint a clearer picture but I don't think it would be prudent. So let's work with this thought experiment which is definitely not out of the ordinary:
We're in a condition where half of the watch team has to be standing watch at a time. As a result, we have a rotation of 5 hours on, 5 hours off, 7 hours on, 7 hours off. In addition to standing watch, training has to be conducted, the ship has to be swept, maintenance of equipment needs to get done. As a result during your 5 hours off you try to get this all taken care of so you can sleep during you 7 hours off.
But wait! According to the 3M Navy planned maintenance system you have a spot-check with the Captain in the middle of your 7 hours off. Too bad. But wait! The XO has recently been displeased with the cleanliness level of the ship, so as a result during sweepers all people not on watch have to be sweeping the passageway. Too bad. But wait! The berthing has been dirty lately so when your people are supposed to be sleeping they are being woken up by the cleaning. Too bad. But wait! Half the team is on watch, and conducting flight operations requires us to realign a vital system on the ship. Too bad, looks like the people who are supposed to be sleeping are going to be woken up. But wait! We have to have a division-wide meeting and training for reason X, Y, and Z. Ideally you would schedule this at watch turnover but if it's something involved we can have our watchstanders being distracted so just do it in your offtime.
Been there. Knew my time with the Navy would be coming to an end after three straight nights of 2 hrs sleep. Followed by a maintenance evolution. Finally got a chance to get some decent sleep, but was racked out again because I had left a small discarded tube in the work area. I think back and wonder how the Navy was able to function at all with all of the chaos going on during a normal work day. So much of the chaos was self inflicted.
But wait! According to the 3M Navy planned maintenance system you have a spot-check with the Captain in the middle of your 7 hours off. Too bad. But wait! The XO has recently been displeased with the cleanliness level of the ship, so as a result during sweepers all people not on watch have to be sweeping the passageway. Too bad. But wait! The berthing has been dirty lately so when your people are supposed to be sleeping they are being woken up by the cleaning. Too bad. But wait! Half the team is on watch, and conducting flight operations requires us to realign a vital system on the ship. Too bad, looks like the people who are supposed to be sleeping are going to be woken up. But wait! We have to have a division-wide meeting and training for reason X, Y, and Z. Ideally you would schedule this at watch turnover but if it's something involved we can have our watchstanders being distracted so just do it in your offtime.
You get the idea.