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