Re: 24x7
For our remote sites, we have a designated "power user" on site, who is responsible for normal run-of-the-mill IT problems (toner, keyboards, locked up PCs etc.) plus a cupboard with some replacement PCs and monitors in it.
They escalate it to us, the next morning, if it is more serious. Production line stand-stills are obviously escalated by the site manager, if they can't solve it themselves.
I think, in the 3 years at my current employer, my boss has been dug out of bed twice - he makes sure all OOH calls go through him.