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