Several years ago I attended a seminar on "The affect of Fatigue on Flight-crew Performance". The presenter - a senior airline manager - explained that the findings he was about to deliver had been derived, researched and validated over a three year period by several disciplines including the FAA, CAA, Institute of Aviation Medicine, NASA and several International universities.
The total cost of the research was slightly under $2.5 million
He then spent just over an hour delivering his presentation with the following summary:
1. When people are subjected to long periods without adequate sleep they get tired.
2. When people are tired they tend to make mistakes.
3. In order to reduce the debilitating effect of fatigue, crews should not operate when tired.
So there you are Pointer41, all your questions answered !