As a general guide, there are airlines where I'm happy to entrust my family to their care, there are others that I wouldn't (a current example of that being Adam Air). The former category has had the occasional cock-up or bomb, but as a percentage of people carried it's an adequately-low risk.
Do you trust your driving sufficiently to risk carrying your children in the car? You're far more likely to have a fatal/serious accident driving to/from the airport than you are on the aircraft. That's probably even true with some of the dodgy carriers, given the driving conditions around their operating airports.
I take the same approach as Topbunk's initial response and I'm definitely not a beancounter.