6-7 Averaged errors in cubic design response surface approximations of probabilistic
sufficiency factor, safety index and probability of failure at 51 points on the curves
of tar get reliability ................. ...............76................
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 ................. ............... ......... ...._..77
6-9 Range of design variables for design response surface approximations of the second
design iteration ........... ..... .._ ...............78....
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) ................. .................7
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 ................. ...............78........... ....
7-1 Random variables in the beam design problem............... ...............85
7-2 Optimum designs for strength failure mode obtained from double loop RBDO .....86
7-3 Design history of RBDO based on sequential deterministic optimization with
probabilistic sufficiency factor under strength constraint for target probability of
failure of 0.00135 ................. ...............86........... .
7-4 Design history of RBDO based on sequential deterministic optimization with
probabilistic sufficiency factor under strength constraint for target probability of
failure of 0.0000135 ................. ...............87........... .
7-5 RBDO using variable fidelity technique with probabilistic sufficiency factor under
strength constraint .............. ...............88....
7-6 Range of design variables for design response surface ................ .....................88
8-1 Amplitudes of geometri c imperfecti on handled by PANDA2 software ................... 94
8-2 Uncertainties in material properties (Al 2219-T87) modeled as normal random
variables .............. ...............94....
8-3 Uncertainties in manufacturing process modeled as uniformly distributed random
design variables around design (mean) value .............. ...............94....
8-4 Deterministic Optimum .............. ...............95....
8-5 Range of analysis response surface approximations (inch) ..........._._... ................ 96