Table 8-5. Range of analysis response surface approximations (inch)
 b h tl t2

 9.5-10.8 1.9465- 2.1515 0.09367-0.1035 0.1198-0.1324


 The accuracy of the ARS is evaluated by statistical measures provided by the JMP

software (Anon. 2000), which include the adjusted coefficient of multiple determination

(R2adj.), and the root mean square error (RMSE) predictor. To improve the accuracy of

response surface approximation, polynomial coefficients that were not well characterized

were eliminated from the response surface model by using a mixed stepwise regression (

Myers and Montgomery 1995).

 A quadratic polynomial of seven has 36 coefficients. The number of sampling

points generated by LHS was selected to be twice the number of coefficients. Table 8-6

shows that the quadratic response surface approximations constructed from LHS with 72

points offer good accuracy.

Table 8-6. Quadratic analysis response surface approximation to the most critical margins
 using Latin Hypercube sampling of 72 points
 Critical margins of load Critical margins of load
 case 1 case 2

 Rsquare adj. 0.9413 0.9986

 RMSE predictor 0.0203 0.00273

 Mean of response 0.4770 0.1986


 The deterministic design is then evaluated under material and manufacturing

uncertainties. The probability of failure of the deterministic optimum under uncertainties

in material properties is shown in Table 8-7. The dominant failure mode is local skin

triangular buckling.