Department of the Air Force Report, 1996

Table 5. Filter Factor Influence on Weighting Percentages
Vehicle Filter • Last Last 10 Last 50 Last Lastl00 Pt. Ratio
(sample) Cons't Point Points Points Half* Points last: first
Atlas 0.96 4.01 33.6 87.2 96.0 98.5 560
(156) 0.97
0.98
0.99
0.995
3.03
2.09
1.26
0.92
26.5
19.1
12.1
9.0
78.9
66.4
49.9
40.9
91.5
82.9
68.7
59.7
96.1
90.6
80.1
72.7
112
22.9
4.7
2.2
Delta 0.% 4.02 33.5 87.5 92.9 98.9 158
(125) 0.97
0.98
0.99
0.995
3.07
2.17
1.40
1.07
26.9
19.9
13.4
10.5
80.0
69.1
55.2
47.6
87.3
78.3
65.6
58.2
97.4
94.3
88.6
84.7
43.7
12.2
3.5
1.9
Titan 0.96 4.00 33.5 87.1 97.1 98.4 1030
(171) 0.97
0.98
0.99
0.995
3.02
2.07
1.22
0.87
26.4
18.9
11.7
8.5
78.6
65.7
48.1
38.5
93.2
85.1
70.5
60.8
95.8
89.6
77.2
68.5
177
31.0
5.5
2.3
* Last half + 1 if sample size is odd
Although the choice of a filter constant cannot be completely objective, use of a value
less than 0.97 or greater than 0.99 produces undesirable weightings. For F = 0.96, for
example, the most recent test result for Titan is weighted 1030 times that for the oldest
test; the last 50 data points receive 87.1 % of the total weighting, leaving only 12.9% for
the first 121 flights; the last 100 flights receive 98.4% of the total weighting thus, in
effect, omitting the oldest 71 flights from the solution.
At the high end of the F spectrum, a value of 0.995 fails to down-weight the old test
•results sufficiently. Using Atlas as an example, the most recent data point (1/31/96) is
weighted only 2.2 times that of the oldest data point (8/14/64). The oldest half of the
data, stretching from 8/14/64 to 3/06/73, receives 40% of the total weight, and the
earliest 56 launches, comprising 36% of the data, receive 27% (100 - 73) of the total
weight. This is not too different from equal weighting of tests, a procedure that fails to
acknowledge the improvements in Atlas reliability that have taken place over a period
of 32 years.
In choosing a value of F, an attempt is made to strike a suitable balance between two
contrary objectives:
(1) to down-weight substantially those failures for which the probability of
occurrence has been greatly reduced through redesign and replacement of
components, improved test procedures, and the like;
9/10/96 21 RTI