5-10 Effects of quality control of EZu On probability of failure for 0. 12 inch-thick (16)s
 laminates............... ...............4

5-11 Effects of quality control of st", sil, E21, and Y12 On probability of failure of 0. 12
 inch-thick (f6)s laminates ................. ...............50........... ....

5-12 Effects of quality control of El, E2, G12, Cl12, Tzero, al, and a2 On probability of
 failure of 0. 12 inch-thick (f6)s laminates ................. ...............50..............

5-13 Effects of quality control of EZu On probability of failure for 0. 1 inch-thick (16)s
 laminates............... ...............5

5-14 Effects of quality control of EZu On probability of failure for 0.08 inch-thick (16)s
 laminates............... ...............5

5-15 Sensitivity of failure probability to mean value of 82u (CV=0.09) for 0. 12 inch-thick
 1(iO) s am inmates .............. ...............52....

5-16 Sensitivity of failure probability to CV of 82u ( E(82u)=0.0154 ) for 0. 12 inch-thick
 (16)s lam inmates .............. ...............52....

5-17 Maximum E2 (milliStrain) induced by the change of material properties El, E2, G12,
 Cl12, Tzero, al, and a2 for 0. 12 inch-thick [f250]s laminate ................. ................. .54

5-18 Probability of failure for 0. 12 inch-thick [ f 250]s laminate with improved average
 material properties (Monte Carlo simulation with a sample size of 10,000,000)....54

6-1 Random variables in the beam design problem............... ...............62

6-2 Range of design variables for design response surface............___ ........._ ......72

6-3 Comparison of cubic design response surface approximations of probability of
 failure, safety index and probabilistic sufficiency factor for single strength failure
 mode (based on Monte Carlo simulation of 100,000 samples) ........._..... ..............73

6-4 Averaged errors in cubic design response surface approximations of probabilistic
 sufficiency factor, safety index and probability of failure at 11 points on the curves
 of tar get reliability ................. ...............74................

6-5 Comparisons of optimum designs based on cubic design response surface
 approximations of probabilistic sufficiency factor, safety index and probability of
 failure .............. ...............75....

6-6 Comparison of cubic design response surface approximations of the first design
 iteration for probability of failure, safety index and probabilistic sufficiency factor
 for system reliability (strength and displacement) ................. .................7