Pan American Airlines....definitely safe!
The truth is is any one safe? Just because an airline is the biggest, has been around the longest, makes the most money etc. doesn't make it bullet proof. Maybe on paper, but it only takes a major incident or world event to turn the tide.
Aviation history is littered with names of airlines who in their heyday where probably thought to survive the toughest of climates.
Food for thought, an interesting discussion though!