# ENAE 483/788D Principles of Space Systems Design Fall, 2002

## Question 8:

For both ENAE 483 and ENAE 788D:

a) The Saturn V launch vehicle flew 13 times with no failures. Given an 80% confidence, what reliability did the Saturn V have?

b) The requirements document for the Apollo program set a 95% chance of mission success on any given mission. Since the launch had to work for mission success, this implies that the Saturn V had to have a reliability of at least 0.95. Given this reliability, what confidence value does this correspond to?

c) The requirements document also set a reliability of 0.999 for crew survival. If the launch vehicle fails, the only means of crew survival is the successful operation of the Launch Escape System, which would pull the Apollo spacecraft away from the exploding booster. If the launch vehicle is 0.95 reliable, which is the minimum required reliability of the LES to meet the 0.999 reliability for crew survival?

d) NASA currently says that the odds of a catastrophic Space Shuttle failure are 1 in 437. To date, there have been 110 successful shuttle missions, and 1 failure. What confidence can be placed on this estimate?

e) The Evolved Expendable Launch Vehicle (EELV) program is aimed at producing two advanced launch vehicles (Atlas V and Delta IV) which will reliably place payloads in orbit. The Delta IV will nominally fly once per month, Down time following a failure will be nine months. Assuming this launch vehicle will fail (on average) once in every thirty missions and that no payloads are lost from the backlog, what surge rate does this system have to have to be marginally resilient?

f) The shuttle general purpose computers are 98% reliable. The primary system uses five computers redundantly, but at least three must be operating for the system to function. The backup computer is a single GPC, which has the same unit reliability. If the overall reliability of the five-computer primary system is the same as the single-unit backup, find the maximum allowable intercorrelation rate.

For ENAE 788D only:

g) Based on the current shuttle record from (c), what reliability could you claim today at an 80% confidence?