Uniform shell designs

Some second-order designs, such as the uniform shell designs (Doehlert [28]), have been proposed which are not based on the central composite design. A more thorough treatment of additional second-order designs can be found in the texts mentioned earlier see Myers [11], Box and Draper [12], Khuri and Cornell [13]. 

D.H. Doehlert, Uniform shell designs. Journal of the Royal Statistical Society, Series C, 19 (1970) 231-239. 

Doehlert, D id (1970), Uniform Shell Designs, Applied Statistics, 19 (3), 231-239. 

Doehlert, D.H. Uniform shell designs. Appl. Stat. 1970,19, 231-239. 

Therefore, the aim of present work is to study the gelling behaviour of K-carrageenan/soy protein systems at neutral pH, under conditions where the protein does not gel (i.e. low protein concentration). To this end a Doehlert uniform shell design for two factors (protein and potassium concentration) was performed. 

A Doehlert uniform shell design for two factors was selected.12 Results were analysed by using the software Statgrafic 5.1. The variables studied were potassium ions (K+) and protein concentration. The real and coded values are shown in Table 1. The three replicates of the central point allowed the error of the methods to be calculated. 

The uniform shell design (7) is a (rhombic) lattice of uniform density in normalized factor space. The design itself is normally just one part of the lattice - a single point and its nearest neighbours. It may be extended in any direction. This includes the possibility of adding additional factors without any adverse effects on the quality of the design. 

The standard uniform shell designs are listed in table 5.22 for 3, 4, and 5 factors. 

Table 5.23 Uniform Shell Design for Characterising the Dissolution Profile of Coated Pellets, as Function of pH, Buffer Concentration and the Stirring Speed... 

For any number of factors k, one of the points of the simplex is the origin, and the other k points he on the surface of a sphere with radius 1.0 centered on the origin, in such a way that the distances between neighboring points are all the same. Each of these points subtracted from the other k points forms k new points, so the design matrix has a total of k +k+1 points. Since the points are uniformly distributed on a spherical sheU, Doehlert suggested that these designs be called uniform shell designs. 

Doehlert D-1 uniform shell designs. To obtain the coded factor levels for a design in k factors select the upper left matrix of k columns and ik +k)l2 +l rows and augment it with the negative of every row except the first, to obtain the full design with k +k+1 rows... 

Journal of Quality Technology, Vol.l2, pp. 214-219 Doehlert, D. (1970) Uniform shell designs. Applied Statistics, Vol.l9, pp.231-239. 

The minimum number of distincts points fV of a uniform shell design for a given number of factors k is ... 

In spite of this, the Doehlert experimental designs are of sufficient quality with regard to these properties, and they have other properties largely making up for it. Consiruciion. The Doehlert uniform shell designs are generated from a simplex. 

The experimental design of the uniform shell design allowing to calculate the coefficients of a second-degree response surface model is ... 

The experimental design of the uniform shell design is Table 25... 

Let us study the second approach. Let us examine the Doehleit uniform shell design fork = 3 (after rearrangement of the rows). 

Doehterl U.H. (1970). Uniform shell designs. Appl. Stat., 19. 231-239, Roquemore K.G. (1976). Hybrid designs for quadratic respon.se surfaces. Technometrics. 18. 419-424. 

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