Published Report (DOT/FAA/CT-94-36)

lunder resulting in a TCV is highest when the blundering
aircraft is slightly ahead (closer to the threshold) of the
adjacent aircraft.
For analytical purposes, an alignment l1window8l will be defined
for blunders which would result in a TCV if the controllers did
not intervene. These blunders were considered to be "at risk" of
resulting in a TCV. The length of the window depends on the
ratio of the speeds and the blunder angle, and it can be shown
analytically to be independent of the runway separation. The
speeds used in the simulation ranged from 120 kn to 227 kn. The
120 kn was the slowest speed of a blundering aircraft, and the
227 kn was the fastest speed of an evading aircraft.
Assuming that either aircraft could be traveling at any speed
between these two numbers, then the ratio of speeds ranged from
120/227 = .53 to 227/120 = 1.89. Using the maximum speed ratio
(1.89) with a blunder angle of 30 degrees, the maximum window
length was 2279 ft. Therefore, the probability of an "at risk"
blunder, assuming 3 nmi longitudinal separation between aircraft
on the same approach, is given by:
2279 = -125 = 1 Itat risk" WCB
3 x 6076 8 WCB's
Therefore, about one aligned approach occurs for every eight
approaches executed.
A review of the data indicated that a total of 186 WCB's were
initiated when the blundering aircraft was in the alignment
window. Of the "at risk" WCB's, two resulted in an actual TCV.
Using a 99 percent confidence interval to compute the upper bound
for the probability of a TCV given an llat risk" WCB, the upper
bound would be 0.049, or:
0.049 = 5 TCV's
102 Itat risk" WCB's
The NTSB would evaluate a mid-air collision as two accidents.
Therefore, one TCV would equal two accidents:
1 TCV
2 ACC
Finally, using the data cited above, the number of blunders which
could occur in the operational environment, before the target
probability of 1 fatal accident in 25 million approaches, can be
calculated. The calculation is shown on the following page:
42