Applied Statistics and Probability for Engineers

566 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS (a) Estimate the factor effects. (b) Form a tentative model by examini ...

14-10 RESPONSE SURFACE METHODS AND DESIGNS (CD) 567 14-54. An article in Rubber Chemistry and Technology (Vol. 47, 1974, pp. 825 ...

568 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS MIND-EXPANDING EXERCISES 14-55. Consider an unreplicated 2kfactorial, ...

14-10 RESPONSE SURFACE METHODS AND DESIGNS (CD ONLY) 569 MIND-EXPANDING EXERCISES x 1 x 2 yx 1 x 2 y  1  1 211 0 1.5 168 1  ...

570 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS IMPORTANT TERMS AND CONCEPTS In the E-book, click on any term or conce ...

14-2 SOME APPLICATIONS OF EXPERIMENTAL DESIGN TECHNIQUES (CD ONLY) Experimental design is an extremely important tool for engine ...

number of defects, and assist in determining which process variables should be carefully con- trolled during manufacturing to pr ...

run at two levels each at 10F and 0.5 hours above and below the current operating condi- tions. This two-factor factorial desig ...

those specific levels. Now we briefly consider the situation where one or more of the factors in a factorial experiment are rand ...

14-5 EXAMPLE S14-1 Two factors that may influence the breaking strength of cloth are being studied. Four test machines and three ...

which would be compared to f0.05,6,123.00, and so H 0 : ^2 0 cannot be rejected. TheP-value for this ratio is P0.2338. To ...

In this model, iis a fixed effect defined such that , is a random effect, the interaction term ()ijis a random effect, and i ...

The variance components ^2 , ^2 , and ^2 may be estimated by eliminating the first equa- tion from Equations S14-8, leavin ...

14-9 the test statistics for main effects and interactions have been constructed properly using Equations S14-9 through S14-11. ...

factorial points, and let be the average of the nCrun at the center point. If the difference is small, the center points lie on ...

design (with a single replicate of each factorial run) augmented with five center points. The design and the yield data are show ...

where represents the noise or error observed in the response Y. If we denote the expected re- sponse by E(Y)f(x 1 , x 2 ), t ...

response function, analysis of the fitted surface will be approximately equivalent to analysis of the actual system. RSM is a se ...

increases most rapidly. This direction is normal to the fitted response surface contours. We usually take as the path of steepes ...

EXAMPLE S14-3 In Example S14-2 we described an experiment on a chemical process in which two factors, reaction time (x 1 ) and r ...