It's very readable and goes into a bunch of other issues at NASA at the time beyond the O-ring failure, which Feynman treats as a symptom of more general engineering and cultural problems.
Feynman is well-known for his TV appearance where he dramatically demonstrated what happened with the O-rings, live...but in his memoir, "What Do You Care What Other People Think?", he credits being inspired by General Kutyna, who had asked him to join the commission. Feynman describes that a random comment from Kutyna led him down the path of revelation:
> Then he says, “I was working on my carburetor this morning, and I was thinking: the shuttle took off when the temperature was 28 or 29 degrees. The coldest temperature previous to that was 53 degrees. You’re a professor; what, sir, is the effect of cold on the O-rings?” “Oh!” I said. “It makes them stiff. Yes, of course!” That’s all he had to tell me. It was a clue for which I got a lot of credit later, but it was his observation. A professor of theoretical physics always has to be told what to look for. He just uses his knowledge to explain the observations of the experimenters!
However, Feynman admits at the end of his multi-chapter account of serving on the commission that Kutyna had coyly played Feynman:
> Another thing I understand better now has to do with where the idea came from that cold affects the O-rings. It was General Kutyna who called me up and said, “I was working on my carburetor, and I was thinking: what is the effect of cold on the O-rings?” Well, it turns out that one of NASA’s own astronauts told him there was information, somewhere in the works of NASA, that the O-rings had no resilience whatever at low temperatures—and NASA wasn’t saying anything about it. But General Kutyna had the career of that astronaut to worry about, so the real question the General was thinking about while he was working on his carburetor was, “How can I get this information out without jeopardizing my astronaut friend?” His solution was to get the professor excited about it, and his plan worked perfectly.
If we take Feynman at his word, to me this is a great description of how science and bureaucracy and invention (and, sometimes, disaster) works: it's not always just random eurekas, or study-real-hard-and-you'll-figure-it-out...sometimes the information is already well-known, and obvious, but for various logistical/political/bureaucratic reasons, it isn't immediately disseminated or explored.
via: Feynman, Richard P. (2011-02-14). "What Do You Care What Other People Think?": Further Adventures of a Curious Character (Kindle Locations 2923-2930). W. W. Norton & Company. Kindle Edition.
"Kutyna: On STS-51C, which flew a year before, it was 53 degrees [at launch, then the coldest temperature recorded during a shuttle launch] and they completely burned through the first O-ring and charred the second one. One day [early in the investigation] Sally Ride and I were walking together. She was on my right side and was looking straight ahead. She opened up her notebook and with her left hand, still looking straight ahead, gave me a piece of paper. Didn't say a single word. I look at the piece of paper. It's a NASA document. It's got two columns on it. The first column is temperature, the second column is resiliency of O-rings as a function of temperature. It shows that they get stiff when it gets cold. Sally and I were really good buddies. She figured she could trust me to give me that piece of paper and not implicate her or the people at NASA who gave it to her, because they could all get fired."
Engineers at Rocketdyne, the manufacturer, estimate the total probability [of catastrophic failure] as 1/10,000. Engineers at Marshal estimate it as 1/300, while NASA management, to whom these engineers report, claims it is 1/100,000. An independent engineer consulting for NASA thought 1 or 2 per 100 a reasonable estimate.
— Personal observations on the reliability of the Shuttle (Rogers Commission Appendix F) by R.P. Feynman
Actual statistics from the life of the shuttle, last flown as STS-135 8 - 21 July, 2011:
Presumably, those estimates are just for the Space Shuttle Main Engines (SSME/RS-25), give that's what Rocketdyne was manufacturing and propulsion is one of Marshall Spaceflight Center's fortes.
If you still haven't read Richard Feynman's appendix to the Rogers Commission report on the Challenger disaster, here's the closing sentence: For a successful technology, reality must take precedence over public relations, for nature cannot be fooled.
It's very readable and goes into a bunch of other issues at NASA at the time beyond the O-ring failure, which Feynman treats as a symptom of more general engineering and cultural problems.