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