An experimenter performs as 253 fractional factorial design

An experimenter performs as 2^5-3 fractional factorial design with generators I=234 and I=135. After analyzing the results from this design he decides to perform a second 2^5-2 design exactly the same as the first but with signs changed i column 3 of the design matrix.

(a) How many runs does the first design contain? (b) Give a set of generators for the second design. (c) What is the resolution of the second design? (d)What is the defining relation of the combined design? (e) What is the resolution of the combined design? (f) Give a good reason for the unique choice of the second design.

Solution

(a) 4

No. of runs required = 2^k = 2^2 = 4