Lattice designs

For example, the book by Gomez and Gomez describes many possible designs such as the Latin square and the lattice designs. The former can handle simultaneously two known sources of variation among experimental units. Chapters deal with Sampling in experimental plots, and the Presentation of research results. ... 

The factor space representing these components can be formed by a triangle where each vertex represents a pure component. Measurements of the criteria of mixtures of the three components are made at regular points (according to a simplex lattice design) in the factor space (Figure 4.16). 

Figure 4.16 Simplex lattice design for a special cubic model with ten...

J. W. Gorman and J.E. Hinman, Simplex lattice designs for multicomponent systems, Technometrics, 4 (1962) 463-487. 

The Bravais or space lattice does not distinguish between different types of local atomic environments. For example, neighbouring aluminium and silicon both take the same face-centred cubic Bravais lattice, designated cF, even though one is a close-packed twelve-fold coordinated metal, the other... 

All the possible icosahedral surface lattice designs were enumerated by counting the ways in which the equilateral triangular net could be folded into polyhedra with icosahedral symmetry (called icosadeltahedra ). The vector between a neighbouring pair of V5s of any icosadeltahedron must be a lattice vector of the triangular net. 

Simplex lattice design Quantitative Mixture problems, regression models of second and higher orders... 

The most frequently used mixture-"composition-property designs of experiments belong to simplex-lattice designs suggested by Scheffe [5], The basis of this kind of designing experiments is a uniform scatter of experimental points on the so-called simplex lattice. Points, or design points form a [q,n] lattice in a (q-1) simplex, where q is the number of components in a composition and n is the degree of a polynomial. For each component there exist (n+1) similar levels Xp0,l/n,2/n.1 and all... 

Table 3.13 Number of design points of simplex lattice designs...

The number of trials of simplex lattice designs, which depend on the number of components and the degree of regression model, is given Table 3.18. 

The experiment has been realized by a simplex lattice design matrix for the fourth-degree model. This model has been chosen, for in case a lower model order is adequate, the excessive points become control points. 

N -is total number of points in a simplex lattice design, including the control point u-is current number of points in a simplex lattice design ... 

Check of lack of fit of the obtained regression model is done in additional control points, Table 3.22, since the simplex lattice design is saturated. 

---