### Table V: Estimates of the unreliability and its sensitivies for di erent time horizons t for the balanced system.

1994

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### Table 2: Error ratios (maximum errors): k = 2: Problem(a) Note that we have not included results (for some of the smaller meshes) when COLNEW was not able to obtain convergence of the Newton iteration on the nonlinear discrete system corresponding to the given mesh. Thus, for example, there is no entry in Table 3 for N = 4. Note also that as the accuracy of the approximate solutions begins to approach that of the reference solution, the estimate of the global error becomes unreliable, and thus the estimates of the convergence rates become irrelevant. From Tables 2-7, we can observe that the expected rates of convergence are being approached by the numerical approximations. From Tables 2-4, we can 35

### Table 5: Unreliability of a MARS FTU in the interval [0; 10] hours. Balanced Failure Biasing Augmented Balanced Failure Biasing Scale Factor Result Error Result Error

"... In PAGE 8: ...3 Unreliability of a MARS FTU Using the governor for balanced failure biasing with exponential transformation we ran a simulation of 100,000 replications to estimate the unreliability of the MARS FTU modeled in Figure 1 using the re- ward structure in Equation 1. The results are shown in Table5 . The numbers in the columns labeled \Re- sult quot; are the point estimates and the numbers in the \Error quot; columns are estimated relative half-widths of the con dence intervals at a con dence level of 99%.... ..."

### Table 4: Sample variance for di erent failure bias values

1999

"... In PAGE 82: ... We used such a xed recovery action in the con gurations Conf2, Conf3, Conf4 and Conf5 mentioned earlier. The unreliability estimates of these con gurations are shown in the Table4 . The failure bias used was 0.... ..."

### Table 4: Sample variance for di erent failure bias values

"... In PAGE 82: ... We used such a xed recovery action in the con gurations Conf2, Conf3, Conf4 and Conf5 mentioned earlier. The unreliability estimates of these con gurations are shown in the Table4 . The failure bias used was 0.... ..."

### Table 3. Unreliability vs. time

2001

"... In PAGE 4: ... The quantitative analysis of the PFT provides the follow- ing results. The system unreliability ( Table3 ) is evaluated as the probability PrfTEg of reaching the TE at time t and has been computed from t = 0 to t = 4 105 h. Time t (h) TE Unreliability U 10,000 8:295 10?4 20,000 1:993 10?3 40,000 5:300 10?3 60,000 9:865 10?3 80,000 1:563 10?2 100,000 2:253 10?2 200,000 7:207 10?2 300,000 1:407 10?1 400,000 2:212 10?1 Table 3.... ..."

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