8-6 Quadratic analysis response surface approximation to the most critical margins
 using Latin Hypercube sampling of 72 points .............. ...............96....

8-7 Probabilities of failure calculated by Monte Carlo simulation with 1x106 Samples 97

8-8 Range of design response surface approximations (inch) .............. ...................97

8-9 Cubic design response surface approximation to the probability of failure and
 probabilistic sumfciency factor (calculated by Monte Carlo sampling of lx106
 sam pl es) ................ ...............97.......... ......

8-10 Optimum panel design............... ...............98.

8-11 Probabilities of failure calculated by Monte Carlo simulation of 1x106 Samples....98

8-12 Uncertainties in material elastic properties (AS4) modeled as normal distribution
 with coeffcient of variation of 0.03 ................ ...............100..............

8-13 Uncertainties in material strength properties (AS4) modeled as normal distribution
 with coeffcient of variation of 0.05 ................ ...............100..............

8-14 Variation of the random design variables around nominal design value ...............100

8-15 Safety factors used in deterministic design .............. ...............101....

8-16 Deterministic Optimum (inch, degree, lb)............... ...............101..

8-17 Quadratic analysis response surface approximation to the worst margins using Latin
 Hypercube sampling of 342 points............... ...............102

8-18 Probabilities of failure calculated by Monte Carlo simulation of 106 samples
 (material and manufacturing uncertainties) ................. ............... ......... ...102

8-19 Design history of RBDO based on sequential deterministic optimization using
 probabilistic sumfciency factor to correct safety factor directly by Equation (8-3)105

8-20 Design history of RBDO based on sequential deterministic optimization using
 probabilistic sumfciency factor to correct safety factor by actual safety margin using
 Equation (8-4) .............. ...............105....

8-21 Design history of RBDO based on DIRECT deterministic optimization with
 probabilistic sumfciency factor correct safety factor by actual safety margin using
 Equation (8-4) .............. ...............108....