The optima found by using the design response surface approximations of Table 6-
6 are compared in Table 6-8. The probabilistic sufficiency factor design response surface
led to a better design than the probability or safety index design response surface in terms
of reliability. The probability of failure of the Pyf design is 0.00314 evaluated by Monte
Carlo simulation, which is higher than the target probability of failure of 0.00135. The
deficiency in reliability in the Pyf design is induced by the errors in the probabilistic
sufficiency factor design response surface approximation. The probabilistic sufficiency
factor can be used to estimate the additional weight to satisfy the reliability constraint. A
scaled design of w = 2.7123 and t = 3.5315 was obtained in section 2.1. The objective
function of the scaled design is 9.5785. The probability of failure of the scaled design is
0.001302 (safety index of 3.0110 and probabilistic sufficiency factor of 1.0011) evaluated
by MCS with 1,000,000 samples.
Table 6-8. Comparisons of optimum designs based on cubic design response surface
approximations of the first design iteration for probabilistic sufficiency factor,
safety index and probability of failure
Desig resonseMinimize objective function F while P 2 3 or 0.00135 > pof
surface of Obj ective Pof/Safety index/Safety factor
Optimafunction F=w~t from MCS of 100,000 samples
w=2.6591,
Probability '9.3069 0.00522/2. 5609/0.9589
t-3.5000
w=2.6473,
Safety index '9.2654 0.00630/2.4949/0.95 19
t-3.5000
Probabilistic w=2.6881,
94084 0.00314/2.7328/0.9733
sufficiency factor t-3.500
The design can be improved by performing another design iteration, which would
reduce the errors in design response surface by shrinking the design space around the
current design. The reduced range of design response surface approximations is shown in
Table 6-9 for the next design iteration. The design response surface approximations