Question

consider a 2^6-2 with 16 runs design. using E=ABC, F=BCD we get I=ABCE=BCDF. if we drop factor F. the new design should be 2^5-1. construct new design with all signs and write down the alias structure.

no data needed

Answer 1

Generate the 2^6−2 design with defining relation I = ABCE = BCDF = ADEF
using method

– Generate a 24 design in the first four factors (A, B, C, and D). Then, choose aliases for
E and F that can be expressed only in terms of A, B, C, and D. Use these to determine
the columns for E and F.

E = ABC = BCDEF = ADF F = = =

– Now, multiply the appropriate columns to form columns for E and F

In the 26−2 design with defining relation I = ABCE = BCDF = ADEF,
the effects are aliased as follows:

A = BCE = ABCDF = DEF AD = BCDE = ABCF = EF
B = ACE = CDF = ABDEF AE = = =
C = ABE = BDF = ACDEF AF = = =
D = = = BD = ACDE = CF = ABEF
E = = = BF = ACEF = CD = ABDE
F = ABCEF = BCD = ADE ABD = = =
AB = CE = ACDF = BDEF ACD = BDE = ABF = CEF
AC = BE = ABDF = CDEF I = ABCE = BCDF = ADEF