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.