the difficulty is with getting people to remember to inform you. i don't think there's an easy system.

inform, inform, inform!!! the more you tell people the more they are likely to respond.

it's easIER if you have email as you can simply once a week email everyone who was on call in the previous seven days and ask them. otherwise chasing people up is hard.

if you have any central office or noticeboard that everyone visits, have a plastic sleeve with forms in that everyone can fill out.

if calls must go through switchboard, you could get switchboard staff to keep a tally of every time they ring for out of hours physio and you could check that against known call outs.