As has been noted elsewhere, I come from a different heritage that most of you medical folks, but when I was a wet-behind-the-ears Ensign I was taught something that still rings true.
In an operational environment, there is a point at which you relieve someone who can't stand the watch rather than endanger others; that is the responsibility of leaders. Second to that is that leaders accept accountability for the actions of those on their watch.
I was the OOD during the Rev watch [0400-0700] on a warship in the Pacific when I looked up from the chart and saw a *massive* container-ship coming out of the fog close aboard our starboard bow - I glanced to the JOOD who had the Conn, and the fool had his back to the bow and was chatting with the helmsman like it was cocktail hour.
I took the Conn, ordered an aggressive maneuver to get us out of harms way, and then had to explain to the Old Man why he got thrown around in his rack in the early morning.
The JOOD and I then went to a bridge wing where I secured the WTD and we had a heart-to-heart chat about my expectations if he ever stood watch with me again.
The point is this; operational systems are expected to operate - if their status looks like a traffic light, you loose the confidence of others, and you should be expected to be relieved and replaced.