My mind goes to the debugging stage after the dust has settled... how would a rocket scientist determine the cause of a RUD like this?
The basic link is: http://www.nasa.gov/columbia/home/CAIB_Vol1.html
Start at chapter 2, on page 27. Highlights: "lock the doors" (page 44), the hunt for debris (page 45), reconstruction (page 47, 72, 74ff). It's really an amazing engineering detective story.
The fault tree analysis methodology is on page 85ff.