hardware improvements that have taken place through the years. For samples
approaching 100 or so, it seriously over-weights the old data and under-weights the
more recent events. Although equal weighting does not seem suitable for this
application, it could be appropriate in other large-sample situations, for example,
predicting the failure probability of devices that are all manufactured at the same time
by the same process, and tested to the same standards.

                      Table 4. Comparison of Weicllting Percentages
 Sample                  Last+      Last5     Last 10    Last 25 !Last 50         Last
   Size      Filter*     Point      Points     Points     Points    Points        Half
     4       Expon.      25.8        -          -           -          -         51.0
             Index       40.0        -          -           -          -         70.0
             Equal       25.0         -         -           -          -         50.0
    10       Expon.      10.9       52.5      100.0         -          -         52.5
             Index       18.2        72.7     100.0         -          -         72.5
             Equal       10.0       50.0      100.0         -          -         50.0
    20       Expon.        6.0      28.9       55.0         -          -         55.0
             Index         9.5      42.9       73.8         -          -         73.8
             Equal         5.0       25.0      50.0         -          -         50.0
  100        Expon. ·      2.3       11.1      21.1       45.7      73.3         73.3
             Index         2.0        9.7      18.9       43.6      74.8         74.8
             Equal         1.0        5.0      10.0       25.0      50.0         50.0
  200        Expon.        2.0        9.8      18.6       40.4      64.7         88.3
             Index         1.0        4.9       9.7       23.4      43.7         74.9
             Equal         0.5        2.5       5.0       12.5      25.0         50.0
  500        Expon.        2.0        9.6      18.3       39.7      63.6         99.4
             Index         0.4        2.0       4.0        9.7      19.0         75.0
             Equal         0.2        1.0       2.0        5.0      10.0         50.0
 1000        Expon.        2.0        9.6      18.3       39.7      63.6         99.996
             Index         0.1        1.0       2.0        4.9       9.7         75.0
             Equal         0.1        0.5       1.0        2.5       5.0         50.0
* F = 0.98 for exponential filter
+ "Last" refers to the most recent data point
The index-count filter has serious deficiencies when applied to either small or large
samples of missiles and space vehicles. For small samples, too much emphasis is
placed on recent data. For a sample of four, 40% of the total weight is given to the last
test, and 70% to the last two tests. For a sample of ten, 18.2% of the total weight is
given to the last test and 72.7% to the last five tests. The reliability improvement rate
implied by these weightings seems too optimistic unless there were serious design
flaws in the early configurations that were discovered and corrected. Since many types
of failures surely exist that occur only once in 50 or once in 100 or more launches, the
tenth launch may be no better than the first for predicting the probability of occurrence
of such failures. For large samples, the index-count filter under-weights current data


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