3. Construct a 273 factorial fractional design with as high a resolution possibl

Question

3. Construct a 273 factorial fractional design with as high a resolution possible. a) b) Write down the complete calculation matrix for this design showing all 2, 3, and 4 factor interactions. Write down the design matrix for this design showing all seven main effects. c) d) e) What are the generators for your design? What are the defining relations and aliases for your design? What are the effects confounded with the main effect of variable C in your design? What are the effects confounded with the two-factor interaction CD in your design?

Explanation / Answer

Factors occur equal number of times at low and high levels; interactions …

sample size for 2-factor interactions = 1/8 of total.

1 2 3 4 5=123 6=234 7=134 A B C D E=ABC F=BCD G=ACD -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 -1 1 -1 1 -1 -1 1 1 -1 1 1 -1 -1 -1 1 1 -1 -1 1 -1 1 1 1 1 -1 1 -1 -1 1 -1 -1 1 1 -1 -1 -1 1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 -1 -1 1 1 1 -1 -1 1 -1 1 1 -1 1 1 1 -1 1 -1 -1 -1 -1 -1 1 1 1 -1 -1 1 -1 1 1 -1 -1 1 -1 1 1 1 -1 1 -1 1 1 1 1 1 1 1

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