"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 by R.P. Feynman
http://science.ksc.nasa.gov/shuttle/missions/51-l/docs/roger...
Empirical post script (as of STS-132 2010-05-26)
Total launches 131
Failures 2
Successes 129
Failure rate: 1.5%
If you read the report, you will find that NASA declared a reliability number that the shuttle was to meet (1/100,000), and then backed into the calculations that justified that reliability number. In other words, it was top-down, rather than bottom-up. IMHO, bottom-up tends to be pessimistic, but top-down tends to be be a figment of management's imagination. In his report, Dr. Feynman pointed out that many of the calculations had reliability figures that, while not necessarily wrong, were so small as to be impossible to validate... but that was the number necessary to generate the 1/100,000 roll-up (actually, rolled-down) number.