Draper-Lawrence design

The triangular coordinate system (Xlt X2, X3) is related to the rectangular one (Zlt Z2) as follows  

When the whole of the diagram is explored, m=l and when local areas of the diagram are explored, m l. Design points for ternary system are selected (in the coordinates Z1 Z2) from the following sets  

1) Vertices of a triangle similar to a given concentration triangle and centered on the origin, with side of length p  

3) Vertices of a square centered on the origin, with sides 2a parallel to axes ( a, a)  

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The arrangement of the points in the concentration triangle is shown in Fig. 3.26. Draper and Lawrence suggested for second-order polynomials of Eq. (3.125) as applied to ternary systems, the designs containing from 8 to 15 design points. Parameters for the Draper-Lawrence designs (in fractions of m) at q=3, ni=2 and n2=3, are summarized in Table 3.46. 

After one or other Draper-Lawrence design has been constructed for quaternary systems, polynomials are obtained in three independent variables Z3, Z2 and Z3 of first degree (n l, for n2=2) ... 

A Draper-Lawrence design containing 13 points is performed (Table 3.51). It is convenient to treat the subregion studied as a concentration triangle in the new coordinate system (X], X2, X3 ) ... 

Geometric interpretation of design points in Draper-Lawrence design is shown in Fig. 3.29. 

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