Doehlert design variables

Doehlert designs and response surface models were developed to evaluate the effects and interactions of flve variables on the extraction of Mn in a flow-injection device. 

An on-line coupling of a flow-injection system with the AAS technique was proposed. The full factorial design was used to ascertain the relevant variables which were then optimised using a Doehlert design (pH and concentration of the complexing agent)... 

FAAS A four-variable Doehlert design was used to optimise a... 

Figure 5.13 Expansion of the Doehlert design by addition of a 3" variable factor (added experiments are shown by filled squares in the 3-D diagram on the right-hand side).

An important property of the Doehlert design lies in the number of levels that each variable takes. In the normal form of the design the number of levels of Xi, X2, Xj is 5, 7, 3. In fact, no matter how many variables we have in the design, the minimum num.ber of levels will be 3, then 5, 7,. .. 7. The levels are evenly spaced. Thus in the case of 5 variables the numbers of levels are 5, 7, 7, 7, 3. So if there are difficulties in adjustment of the levels of a given factor, then it would be as well to set it to the variable that has only 3 levels in the design. 

Table 21. A Doehlert design with 2 variables in coded units.

Differing number of levels of variables. The Doehlert design is an asymmetrical design the first variable is at five levels, the last one at three levels, and all of the others (except for Jt = 2) at seven levels. 

The graphite furnace temperature program was optimised by response surface methodology (RSM) using a Doehlert design for three variables. 

Figure 8 A Doehlert design for two variables. Experiments 8, 9, and 10 are added to obtain a new design in that direction...

The Doehlert Design [6], like the Central Composite Design, allows estimating the coefficients of a model containing linear terms, interactions and quadratic terms. Table 13 reports the experimental matrix for two and three variables, and Figure 14 shows their graphical representation. 

TABLE 13 Doehlert Design for Two Variables (Experiments 1-Variables (Experiments 1-13) -7) and Three... 

FIGURE 14 Graphical representation of a Doehlert Design for (A) two and (B) three variables. 

FIGURE 15 Sequentiality of a Doehlert Design with two variables. 

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. 

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. 

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. 

A 2-level full design and a 2-Doehlert matrix design were used to optimise a preconcentration procedure where interaction between the four relevant variables could not be disregarded. 

S. L. C. Ferreira, A. S. Queiroz, M. S. Fernandes and D. C. Dos-Santos, Application of factorial designs and Doehlert matrix in optimisation of experimental variables associated with the preconcentration and determination of vanadium and copper in seawater by inductively coupled plasma optical emission spectrometry, Spectrochim. Acta B, 2002, 57B(12), 1939-1950. 

Four variables were optimised to preconcentrate V and Cu by combining full factorial and Doehlert matrix designs. 

Five variables were considered in a full factorial and a Doehlert matrix design to study an online preconcentration procedure. 

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