I have had positions where this was the only option for a day off. Being on-call 24/7 pulls you down and even your "days off" are filled with calls. The only way to get any rest was to call in sick, turn off the cell and pager, and rejuvenate. Some companies don't care that only one person is on-call as long as it keeps their costs down. Some times you have to do what is necessary for your own health and sanity. That is also the reason I found a new position.
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