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

2.3 BASIC RISK EQUATION
A TCV will occur when two aircraft are aligned in such a way that
a TCV is possible and simultaneously a WCB occurs. Intuition
suffices to prove that an alignment window exists during which a
TCV is possible if a worst case blunder occurs. If the aircraft
are not within this alignment window then the blundering aircraft
would pass harmlessly ahead or behind of the evading aircraft
without any evasive movement of the evading aircraft. Likewise,
it is obvious that a TCV can only occur when a blunder turns into
a worst case blunder. Hence a TCV can only occur when the
aircraft are properly aligned during a blunder which results in a
worst case blunder. In mathematical set theory, this means that
the set of TCV's is a subset of the intersection of the set of
aligned approaches with the set of 30° blunders and the set of no
response blunders.
Although a TCV does not
simplicity and in order
existing accident rate,
in a collision and that
necessarily result in a collision, for
to equate the probability of a TCV to the
it will be assumed that a TCV will result
a collision will result in the loss of
both aircraft. Therefore, in order to simplify the analysis, a
TCV will be assumed to result in two fatal accidents.
Using the notation P(event) to indicate the probability that an
event will occur and P(event 1 I event 2) to indicate the
probability that event 1 will occur given that event 2 has
already occurred, the discussion above indicates that the
probability of a collision may be written as:
P(col1ision) = P(TCV)
= P(TCV and aligned and WCB and blunder)
= P(TCV I aligned and WCB and blunder) x
P(a1igned I WCB and blunder) x
P(WCB I blunder) x P(b1under).
In order to compute the probability of a collision or TCV it is
necessary to compute or estimate four factors. The first factor,
P(TCV I aligned and WCB and blunder) may be estimated from data
collected during the simulation of this study. The simulation
is designed to determine the probability that a TCV will occur
when an aligned WCB occurs. The second factor, P(a1igned 1 WCB
and blunder) may be estimated by analytical means. The third
factor, P(WCB I blunder) is not easily estimated, but bounds may
be placed on its possible variation. The fourth factor,
P(b1under) is even more difficult to estimate since it is
extremely small. Since P(TCV) depends on two factors whose
estimation is in doubt, it is desirable to eliminate at least one
of the doubtful factors. From historical data the probability of
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