Montgomery (2012) described a 2^4€“1fractional factorial design used to study four factors in a chemical process. The factors are A = temperature, B = pressure, C = concentration, and D = stirring rate, and the response is filtration rate. The design and the data are as follows:

(a) Write down the alias relationships.

(b) Estimate the factor effects. Which factor effects appear large?

(c) Project this design into a full factorial in the three apparently important factors and provide a practical interpretation of the results.

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Treatment Run A B C D=ABC Combination Filtration Rate 1 (1) 45 ad 100 3 bd 45 4 ab 65 cd 75 6. 60 ac bc 80 abcd 8. 96 + + I + II + + + + +