Z shift was an apparently two-man, low-priority maintenance team aboard the JMC ship Red Dwarf.
Third Technician David Lister (the lowest ranking member of Red Dwarf) was assigned to Z shift under the command of Second Technician Arnold Rimmer (the second lowest ranking member on the ship). This "graveyard shift" was occasionally and begrudgingly supervised by Second Officer Frank Todhunter, who had to deal with Rimmer's many complaints about Lister.
The two Z Shift workers, Rimmer and Lister, were also bunked up together, as crewmen of equal rank frequently were.
Z Shift dealt with cleaning the Vending Machines, such as making sure the nozzle was not clogged with chicken soup, and that the artificial intelligence of the Vending Machines was not wonky so that the Officers would get what they asked for. Z Shift also worked fixing "sticking" or jamming doors, repairing faulty "porous circuits" in the Botanical gardens, and other tasks deemed too menial for the Skutters - either because as Lister puts it, it was beneath the Skutters or because the Skutters have a better trade union than Z Shift. (RD: The End) Lister also worked Waste Disposal occasionally, jettisoning the garbage pods, but Rimmer never did this work. (RD: Waiting for God)
When Lister smuggled a pet cat aboard and got put in stasis as punishment, Rimmer was left alone on Z Shift. Rimmer therefore blamed Lister when Rimmer working alone did not repair a Drive Plate properly, resulting in the accident which killed the crew. Why such an important job was left to an unattended Rimmer is a mystery, however.(RD: The End)
Trivia
The exact number who are a part of Z Shift varies depending on the source. In the novel Infinity Welcomes Careful Drivers, there are a number of technicians such as Petrovich who are a part of this shift.
In the television series, only Rimmer and Lister appear to be a part of it. In a deleted scene from the Series IV episode "Justice", Lister claimed that he was the only technician in Z shift besides Rimmer because "all the others requested transfers."