Table 6-6. Comparison of cubic design response surface approximations of the first
 design iteration for probability of failure, safety index and probabilistic
 sumfciency factor for system reliability (strength and displacement)
 16 Latin Hypercube sampling points + 4 vertices
 ErrorStatiticsProbability Safety index Probabilistic
 response response suffciency factor
 surface surface response surface
 R"a4 0.9231 0.9887 0.9996
 RMSE Predictor 0.1234 0.3519 0.01055
 Mean of Response 0.3839 1.3221 0.9221
 APE (Average Percentage
 Error=RMSE 32.14% 26.62% 1.14%
 Predictor/Mean of Response)
 APE in Pof
 (=RMSE Predictor of 32.14% 10.51% N/A
 Pof/Mean of Pof)


 It is seen that the R2adj of probabilistic sufficiency factor response surface

approximation is the highest among the three response surface approximations, which

implies probabilistic sufficiency factor design response surface approximation is the most

accurate in terms of averaged errors in the entire design space as shown by Table 6-2.

The critical errors of the three design response surfaces are also compared. For each

design response surface approximation, 51 test points were selected along a curve of

target reliability (probability of failure = 0.00135). The average percentage errors at these

test points, shown in Table 6-7, demonstrate that the probabilistic sufficiency factor

design response surface approximation is more accurate than the probability of failure

and safety index response surface approximations.

Table 6-7. Averaged errors in cubic design response surface approximations of
 probabilistic sufficiency factor, safety index and probability of failure at 51
 points on the curves of target reliability
 Design Response Probability of Probabilistic
 Safet Index (Pof
 Surface of failure ae sufficiency factor
 Average Percentage
 Error in Probability 334.78% 96.49% 39.11%
 of Failure