simulation. If a probability of failure of 0.2844 is to be calculated by Monte Carlo
simulation of 100,000 samples (the mean probability of failure in Table 6-3), the standard
error due to the limited sampling is 0.00143. The RMSE error of the probability design
response surface is of 0. 1103. Thus the error induced by the limited sampling (100,000)
is much smaller than error of the response surface approximation to the probability of
failure .
Table 6-3. Comparison of cubic design response surface approximations of probability of
failure, safety index and probabilistic sufficiency factor for single strength
failure mode (based on Monte Carlo simulation of 100,000 samples)
16 Latin Hypercube sampling points + 4 vertices
Error Statistics Probabilistic
Probability RS Safety index RS sufficiency factor
RS
R2adj 0.9228 0.9891 0.9999
RMSE Predictor 0.1103 0.3027 0.002409
Mean of Response 0.2844 1.9377 1.0331
APE (Average
Percentage
Error=RMSE 38.78% 15.62% 0.23%
Predictor/Mean of
Response)
APE in Pof
(=RMSE Predictor of 38.78% 12.04% N/A
PoflMean ofPof)
The probabilistic sufficiency factor design response surface has an average error
less than one percent, while the safety index design response surface has an average error
of about 15.6 percent. It must be noted, however, that the average percent errors of the
three design response surface cannot be directly compared, because one percent error in
probabilistic sufficiency factor does not correspond to one percent error in probability of
failure or safety index. Errors in safety index design response surface were transformed to
errors in terms of probability as shown in Table 6-3. It is seen that safety index design