Doehlert experimental designs

A note is in order here to stress that a special form of experimental designs can be used for optimization. They are known as Doehlert designs, of which several applications are reviewed in Table 2.34. As this chapter is intended at an introductory level, no further details will be give here. 

Fig. 3 Application of the Doehlert experimental design to optimize a MIP for propranolol with respect to the type of cross-linker (EDMA or TRIM) and the degree of cross-linking, (a) Three-dimensional representation of response surfaces for the percentage of bound [3H]propanolol to the molecularly imprinted polymer (MIP) and the corresponding non-imprinted control polymer (NIP), (b) Contour plot of the function describing binding of [3H]propanolol to MIPs relative to the degree and the kind (bi or trifunctional) cross-linking. The values were corrected for non-specific binding to the non-imprinted control polymer. Adapted from [31] with kind permission from Springer Science + Business Media...

Vojnovic, D., D. Chicco, and H. El. Zenary, 1996. Doehlert experimental design applied to optimisation and quality control of granulation process in a high shear mixer, hit. J. Pharm. 145 203-213. 

Composite experimental designs Uniform shell (Doehlert) designs Hybrid and related designs... 

The experimental design for 2 factors is a sub-set of the design for 3 factors, and the design for 3 factors is a sub-set of the design for 4 factors and so on. This is demonstrated later in the chapter, in table 5.22, which gives Doehlert designs for up to 5 factors. 

The second restriction is that of limitations in the number of levels, or of difficulties in setting a factor to certain levels. We have already mentioned this potential problem when discussing the Doehlert experimental design. If the model order in a certain factor is d, then this factor must take at least d + 1 levels. Thus for a second-order model at least 3 levels are required, normally equidistant. If it becomes necessary to minimize the number of levels for more than 1 factor, this may mean choosing a design with all factors taking 3 levels. The possible designs... 

Imandi, S.B. V.V.R. Nabdaru S.R. Somalanak H.R. Garapati. Optimization of medium constituents for the production of citric acid from byproduct glycerol using doehlert experimental design. Enzyme Microb. Technol. 2007, 40, 1367-1372. 

Doehlert designs comprise another class of experimental designs, with which different factors can be studied at different numbers of levels (Doehlert, 1970 Doehlert and Klee, 1972 Massart et al., 1997 Ferreira et al., 2004). They are attractive for treating problems where specific information about the system indicates that some factors deserve more attention than others, but they also have other desirable characteristics. 

DOEHLERT, D. H. and KLEE, V. L. Experimental designs through level reduction of a D-dimensional cuboctahedron. Discrete Math. 2, 1972, pp. 309-334. 

The most often u.sed experimental designs are the composite designs (lO,to, the Doehlert designs (10,13), the hybrid designs (14), and the Bo.x-Benkhen designs (15). 

The Doehlert designs have none of the conventional properties of the response surface experimental designs (isovariance by rotation, cmhogonality, uniform precision, etc.). It can indeed be shown by calculation that ... 

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. 

Factorial design and Doehlert designs were used to determine trace lead in environmental samples. The effect of foreign ions was evaluated using a fractionary factorial experimental design. 

It is possible to add a new variable after having performed a first experimental design. By looking at Table 13 and Figure 14, it can be seen that experiments 1-7 all have the third variable at level 0. These are the experiments for a Doehlert Design with two variables. If a third variable later comes into mind, it is possible to add experiments 8-13 (in this case one must also be careful with the block effect). Of course, in the first set of experiments the forgotten variable should have been kept constant at a level that could be both increased and decreased. 

Nde, D.B., Boldor, D., et al., 2015. Optimization of microwave assisted extraction parameters of neem (Azadirachta indica A. Juss) oil using the Doehlert s experimental design. Industrial Crops and Products 65, 233—240. 

M. Zougagh, P. C. Rudner, A. Garcia-de-Torres and J. M. Cano-Pavon, Application of Doehlert matrix and factorial designs in the optimisation of experimental variables associated with the on-line preconcentration and determination of zinc by flow injection inductively coupled plasma atomic emission spectrometry, J. Anal. At. Spectrom., 15(12), 2000, 1589-1594. 

N. Jalbani, T. G. Kazi, M. K. Jamali, M. B. Arain, H. I. Afridi, S. T. Sheerazi and R. Ansari, Application of fractional factorial design and Doehlert matrix in the optimisation of experimental variables associated with the ultrasonic-assisted acid digestion of chocolate samples for aluminium determination by atomic absorption spectrometry, J. AO AC Int., 90(6), 2007, 1682-1688. 

Fig. 6 Doehlert design in three dimensions (factors) showing extension to a new experimental domain.

Table 5.18 Doehlert Design (2 Factors) for Wet Pelletization in a High-Shear Mixer Design A - Experimental Plan - Data for Mean Size [data from reference (9), with permission]...

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