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

e estimated as the ratio of the number of TCV's to the total
number of at-risk blunders. However, when an experiment is
performed from a known Bernoulli process, such as flipping a coin
or rolling a die, it is known that the observed estimate of the
probability will differ from the theoretic or underlying
probability and that different experiments will produce different
estimates of the same underlying probability. Thus the ratio of
TCVIs to at-risk blunders should not be used directly as the
estimate of the underlying probability.
From the theory of Bernoulli processes, confidence intervals of
the underlying probability may be determined from the observed
data. A confidence interval gives a measure of the variation from
the underlying probability that may be observed in experimental
data. Confidence intervals always have a probability or
confidence level associated with them. A confidence interval
might be termed a 0.99 interval. This would mean that if 100
different experiments were performed to estimate the underlying
probability, then it would be expected that about 99 of the
confidence intervals computed from the observed data would
contain the underlying probability.
Formulae exist for the computation of confidence intervals of
Bernoulli probabilities. Since the probability of a TCV is very
small, the appropriate formulae for the upper and lower limits of
a 0.99 confidence interval are as follows:
k
zc(n,y)pY(l-p)n-y = 0.005
y=o
n
C c( n, y)py (1 - p)"-' = 0.005
y= k
The value of the probability, p, must be found using numerical
methods such as Newton's method or the bisection method.
Since in a computation of risk conservatism is extremely
important, the value associated with the upper limit of the
confidence interval is the only one of interest. The upper limit
of a 0.99 confidence interval represents a value which is almost
certainly larger than the actual underlying probability. Thus
use of the upper confidence interval bound will provide a
conservative estimate of the actual probability.
6.0 DETERMINATION OF ACCEPTABLE BLUNDER RATE
With the determination of a target risk, a method of determining
the window of alignment, and a method of estimating the
probability of a TCV during an aligned blunder, the acceptable
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