A few anecdotal words about working on the ship I served on.
First of all there was the work day. 8-4(-ish) Monday through Saturday at sea, Monday through Friday in port. Work performed depended on your department and rating. For example, as an Electrician's Mate (EM), I was part of the group responsible for the maintenance, repair and upgrade of the ship's electrical components while sailors in the Supply department would be loading, unloading, inventorying, and staging cargo. Chain of command was through your division officer and department head (who answered to the XO and CO.)
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Layered on top of this was duty sections. The idea behind duty sections was to ensure that enough of the correctly qualified personnel were on duty to meet the ship's readiness needs. The approach to this varied depending on whether the ship was at sea or in port. Duty ran from morning muster to morning muster (the duty day).
In port, the ship's crew was divided into 3-4 duty sections (sometimes modified for a Department.) The "on" section was required to remain on the ship during the duty day while the "off" sections usually could go on liberty (or even home if we were in our homeport) at the end of the work day. The scheduling of duty sections was also dogged to allow for weekends off.
At sea, duty sections were typically modified to meet a Division's or Department's needs. E-Division (the EMs) was a part of the Engineering department and while at sea, the Department usually ran at two sections.
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The section that had the duty that day was responsible for standing the day's watches. Watches meant manning stations like the ship's electrical switchboard and were typically four hours long (al though 6-8 hr watches were not unheard of.) What watches there were, again, depended on whether we were at sea or in port. Chain of command for watch-standers was separate and ended at the Command Duty Officer (who answered to the XO and CO.)
In port, watch-standing responsibilities varied greatly from department to department; for the Engineering Department, the biggest factor was ship's power or shore power. Ship's power was the same as being at sea for us; shore power meant a minimal number of damage control watches and therefore more liberty for us (usually four sections on shore power.)
At sea, we engineers ran in two sections and everyone stood at least one watch on a duty day, sometimes two.
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And if that wasn't enough, everyone was also assigned a damage control station. Damage control stations were, for the most part, either watch-stations or damage control lockers and were manned during general quarters or emergency situations like fire or flooding. (For these latter emergencies, we had a first responder team we called the Flying Squad that would assess and sometimes handle the emergency before a ship-wide response was required.) Chain of command for DC stations went through the DC Officer, who reported to the CIC and the bridge.
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Well that's not all (man-overboard, lifeboat stations, etc, could still be mentioned) but it gives you a glimpse I hope of how stuff actually works (or at least worked on one ship, many years ago.)