The fading-memory recursive filter, defined by Eqs. (12) and (20), can be applied to launch test results to estimate failure probability. For this application the values to be filtered are the test .outcomes, with 0 representing a successful launch, and 1 representing a failure or anomalous behavior. Given a series of outcomes, the filtered result after each launch in the series represents the estimate of failure probability at that point. Filtered results for two filter-control constants are shown in Table 37 for a hypothetical series of ten launches for which all but the second and fourth flights were successful. Table 37. Filter Application for Failure Probability Index Outcome j[] F = 0.98 lter factor, an Fail. Prob. F =0.90 Filter factor, an Fail. Prob. 1 0 1.0000 0.0 1.0000 0.0 2 1 0.5051 0.5051 0.5263 0.5263 3 0 0.3401 0.3333 0.3690 0.3321 4 1 0.2576 0.5051 0.2908 0.5263 5 0 0.2082 0.3999 0.2442 0.3978 6 0 0.1752 0.3299 0.2132 0.3129 7 0 0.1517 0.2798 0.1917 0.2529 8 0 0.1340 0.2423 0.1756 0.2085 9 0 0.1203 0.2132 0.1632 0.1745 10 0 0.1093 0.1899 0.1535 0.1477 In this example, estimated failure probabilities are shown for two values of the filter constant that force the filter to fade at two different rates. After ten launches the estimated failure probability using F = 0.98 is 0.1899. For the faster fading-memory filter (F =0.90), the result is 0.1477. Both estimates are less than that obtained by equal weighting, since the two failures occurred early in the sequence. Note that after four launches (2 successes and 2 failures) both filtered estimates exceed 0.5, since one of the two failures occ~rred during the fourth flight. If the l's and O's used in the example to represent failures and successes were reversed, the same filter would provide estimates of probability of success. 9/10/96 95
Vision Description (EN)
Page 104 (document pagination 95) presents technical analysis of the fading-memory recursive filter applied to launch test failure probability estimation. The page contains explanatory text describing the filter methodology with reference to Equations (12) and (20), followed by Table 37 displaying filtered results for ten sequential launches using two filter constants (F = 0.98 and F = 0.90). The table demonstrates probability calculations where 0 represents successful launches and 1 represents failures or anomalous behavior. The accompanying text discusses the comparative behavior of the two filter rates and notes that the filter method can be adapted to estimate probability of success by reversing the binary representation.
Descrição Vision (PT-BR)
A página 104 (numeração do documento 95) apresenta análise técnica do filtro recursivo de memória desvanecente aplicado à estimativa de probabilidade de falha em testes de lançamento. A página contém texto explicativo descrevendo a metodologia do filtro com referência às Equações (12) e (20), seguido pela Table 37 exibindo resultados filtrados para dez lançamentos sequenciais usando duas constantes de filtro (F = 0.98 e F = 0.90). A tabela demonstra cálculos de probabilidade onde 0 representa lançamentos bem-sucedidos e 1 representa falhas ou comportamento anômalo. O texto acompanhante discute o comportamento comparativo das duas taxas de filtro e observa que o método de filtro pode ser adaptado para estimar a probabilidade de sucesso invertendo a representação binária.