iteration shown in Table 6-10 are compared in Table 6-11. It is seen that the design
converges in two iterations with probabilistic sufficiency factor response design surface
due to its superior accuracy over the probability of failure and safety index design
response surfaces.
Table 6-11. Comparisons of optimum designs based on cubic design response surfaces of
the second design iteration for probabilistic sufficiency factor, safety index
and probability of failure
Desig reasons Minimize obj ective function F while P > 3 or 0.0013 5 > pof
surfce f Oti. Obj ective_ Pof/Safety index/Safety factor
function F =wt from MVCS of 100,000 samples
w=2.7923,
Probability '9.3368 0.0051 1/2.5683/0.9658
t-3.3438
w=2.6878,
Safety index '9.4821 0.00177/2.916 5/0.9920
t-3.5278
Probabilistic
w=2.6041,
sufficiency '9.5691 0.00130/3.0115/1.0009
t-3.6746
factor
constructed are compared in Table 6-10. It is observed again that the probabilistic
sufficiency factor response surface approximation is the most accurate.
Table 6-9. Range of design variables for design response surface approximations of the
second design iteration
System variables w t
Range 2.2" to 3.0" 3.2" to 4.0"
Table 6-10. Comparison of cubic design response surface approximations of the second
design iteration for probability of failure, safety index and probabilistic
sufficiency factor for system reliability (strength and displacement)
16 Latin Hypercube sampling points + 4 vertices
ErrorStatiticsProbability Safety index Probabilistic
response response sufficiency factor
surface surface response surface
R2a4 0.9569 0.9958 0.9998
RMSE Predictor 0.06378 0.1329 0.003183
Mean of Response 0.1752 2.2119 0.9548
APE (Average Percentage
Error-RMSE Predictor/Mean 36.40% 6.01% 0.33%
of Response)
The optima based on design response surface approximations for the second design