One of the variables in the experiment described in Problem 6-15, heat treatment method (C), is a

Question:

One of the variables in the experiment described in Problem 6-15, heat treatment method (C), is a categorical variable. Assume that the remaining factors are continuous.

(a) Write two regression models for predicting crack length, one for each level of the heat treatment method variable. What differences, if any, do you notice in these two equations?

(b) Generate appropriate response surface contour plots for the two regression models in part (a). 

(c) What set of conditions would you recommend for the factors A, B, and D if you use heat treatment method C = +?

(d) Repeat part (c) assuming that you wish to use heat treatment method C = -.


Problem 6-15

A nickel-titanium alloy is used to make components for jet turbine aircraft engines. Cracking is a potentially serious problem in the final part, because it can lead to nonrecoverable failure. A test is run at the parts producer to determine the effect of four factors on cracks. The four factors are pouring temperature (A), titanium content (B), heat treatment method (C), and amount of grain refiner used (D). Two replicates of a 24 design are run, and the length of crack (in mm x 10-2) induced in a sample coupon subjected to a standard test is measured. The data are shown in the following table:

Replicate Treatment Combination A B C D I II (1) 7.037 6.376 14.707 15.219 11.635 12.089 ab 17.273 17.815 10.403 10.151 ас 4.368 4.098 + bc 9.360 9.253 abc 13.440 12.923 d 8.561 8.951 ad 16.867 17.052 bd 13.876 13.658 abd 19.824 19.639 cd 11.846 12.337 аcd 6.125 5.904 bcd

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