A First Course in Quality Engineering, 2nd Edition

362 A First Course in Quality Engineering

C = AB� Each of the main factors is confounded with a two-factor interac-

tion� In this one-half fractional design, however, the main factors are not

confounded among themselves�

In the above fractional designs, the effects that are confounded with each

other are said to be the alias of each other� Thus, A is the alias of BC, B the

alias of AC, and C is the alias of AB� The basic relationship C = AB, which

was used to generate the 2

3−1

design, is called the “generator” of the frac-

tional design� Another equivalent way of expressing this relationship that

dened the one-half fraction is to multiply both sides of the generator by C

to obtain CC = ABC� Here, A, B, and C represent the column vectors ...