ABSTRACT
In the previous chapter, we studied the simplex lattice design. A distinguishing feature of this design is the location of the experimental points around the boundary of the simplex-that being the vertices and midpoint along the edges. However, there may be times we wish to investigate the interior space of the simplex. This can be achieved by adding experimental points along principal axes. Principal axes are lines extending from the vertex of each pure blend to the center of the opposing face. The experimental points along a principal axis represent equal amounts of all other ingredients except for that ingredient which that principal axis represents. Suppose we have three ingredients x1, x2, and x3 as shown in Figure 25.1. The principal axis for x1 begins at its vertex, as a pure blend, where the proportion for x1 = 1 and ends at the opposing face: the midpoint of the line between x2 and x3 where it is completely absent from the mixture and the proportion for x1 = 0.
