Department of the Air Force Report, 1996

Table 6. Failure Probabilities for Atlas, Delta, and Titan
Predicted Failure Probability*
Vehicle
Atlas
Delta
Flight Phase
0-1
0.022
0.010
Flight Phase
0-2
0.031
0.013
Titan 0.040 0.064
* Exponential filter with F = 0.98
For Delta, the predicted failure probabilities shown in Table 2 for flight-phases O- 1
and O- 2 are the same, since no second-stage failure has occurred in the 125 flights
included in the representative sample. Obviously, this does not mean that the
probability of a Delta second-stage failure is zero. As stated earlier, the choice of F is a
judgment matter with the most reasonable range for F considered to be 0.97 SF S 0.99. j
To- show a difference in failure probabilities between Delta flight phases, a value of
F = 0.98 has been used for flight phases O-1, and 0.99 for flight phases O- 2. It is an
interesting coincidence that the same value of 0.013 is obtained using F = 0.98 and all IDelta configurations (see Table 3). Another way to estimate the Delta second-stage I
failure probability is to calculate an upper confidence limit at some suitable level for an
event that has occurred zero times in 125 trials. At the 80% confidence level, the Ireliability is at least 0.987, so- the failure probability during second-stage bum (flight
phases 1.5 - 2) is no bigger than 0.013.
I5.2 Relative and Absolute Probabllltles for Response Modes I
For Atlas, Delta, and Titan vehicles, failure-response Modes 1, 2, and 3 are much less I
likely to- occur than Modes 4 and 5. Since the probabilities of occurrence for the less-
likely modes may be only one in a thousand or less, such responses may not have
occurred at all in the flight tests of representative configurations. •In fact, in· the I
combined samples for Atlas, Delta, and Titan, only 16 failures have occurred during
flights phases O- 2. None of the 16 resulted in response-modes 1, 2, or 3. Because of
. the small number of failures in the representative configuration samples, the relative
probabilities of occurrence for Modes 1 through 5 have been estimated using results
from all vehicle configurations and launches shown in Appendix D. The rationale for
this approach is that, except for obvious problems that have been corrected, other
changes made through the years to improve vehicle reliability have reduced the
probabilities of occurrence of all response modes more or less proportionally. The
greater significance of more recent vehicle modifications and test results is. accounted
for by using an exponential filter to estimate overall failure probabilities. Thus, if
Mode-1 failures occurred more frequently in the distant past than in recent years, the
weighting process reduces the significance of the earlier Mode-1 responses in the
relative probability-of-occurrence calculations. As tabulated from Appendix D, the
number (count) of failures by response mode and flight phase for Atlas, Delta, Titan,
and Eastern-Range Thor launches are given in Table 7 through Table 10. Thor launches
9/10/96 24 RTI