chapter  4
20 Pages

Two-level factors: logic, reliability, design

There are close connections between two-level factorial designs and various algebraic structures which employ binary representations. We will try to arrive at a point where moving between the representations will give additional insight. The starting point is a set of variables x1, . . . , xd which are binary. We

code these two levels as {0, 1}. Following the analysis of the previous chapters, we represent the set of values of a vector x = (x1, . . . , xd) as a 2d full factorial design, D2d = {0, 1}d. This can be represented as the solutions of

{xi(xi − 1) = 0 : i = 1, . . . , d} Next, we specialize the theory of Chapter 3 to the binary case.