Don't think about counting how many days have passed, more like its an 18 hour routine... instead of a 24 hour routine...instead of sleep for 8 hours then awake for 16, they would be asleep for 8 hours then be awake for 10, then start over. So from an outside perspective your wake-up time rotates.

I think the point was the keep sailors better rested... instead of potentially being awake for 16 hours and a bit groggy, the longest you should be awake (barring sleep disturbances) would be 10 hours. If the whole ship is rotating at this rate, its the same number of crewmen covering the same number of work shifts, but less chances of a sleepy mistake.... in theory