In Myers, Montgomery, and Anderson-Cook (2009), an

Chapter 15, Problem 15.30

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In Myers, Montgomery, and Anderson-Cook (2009), an application is discussed in which an engineer is concerned with the eects on the cracking of a titanium alloy. The three factors are A, temperature; B, titanium content; and C, amount of grain rener. The following table gives a portion of the design and the response, crack length induced in the sample of the alloy. ABCResponse 1 1 1 1 1 1 1 1 1 1 1 1 0.5269 2.3380 4.0060 3.3640 (a) What is the dening relation? (b) Give aliases for all three main eects assuming that two-factor interactions may be real. (c) Assuming that interactions are negligible, which main factor is most important? (d) At what level would you suggest the factor named in (c) be for nal production, high or low? (e) At what levels would you suggest the other factors be for nal production? (f) What hazards lie in the recommendations you made in (d) and (e)? Be thorough in your answer.