Factorial design experimental variable

Figure 9- Average SCC of Np adsorbed per gram of the clino ZBS-15 for a 3 variable factorial design experimental series. Feed was 33.3 SCC/g of zeolite per cycle of U0 N2/60 CH gas.

To gain an insight into which experimental variables influence the course of the reaction, the authors varied four variables in a two-level factorial design. The variables are specified in Table 17.1, and the design is given in Table 17.2. The responses recorded were the yields of the various pyridines. The responses are summarized in Table 17.3. 

Factorial design One method of experimental design that allows interactions between factors to be investigated, i.e. whether changing one experimental variable changes the optimum value of another. 

EXAMPLE 2.6 IDENTIFICATION OF IMPORTANT VARIABLES BY EXPERIMENTATION USING AN ORTHOGONAL FACTORIAL DESIGN... 

Data analysis of factorial designs involves a comparison of the experimental responses at the high and low settings of each variable. The results can be plotted in several different ways to develop an understanding of the effect of changing two or more process variables at a time with regard to reaction yield and quality of the product. 

Elompart et al. (2001), like Jozefaciuk et al. (2003), use a combined R D section (the preferred format in Analytical Chemistry, the journal that published this article). Their R D section describes both preliminary tests and optimization procedures. Results and discussion of the preliminary tests were presented in excerpt 4C results and discussion of the optimization procedures are presented in excerpt 5A. The optimization process used a factorial design in which five experimental parameters were systematically varied and tested to improve the saponification technique. These variables included the concentration of NaOH, the volume of NaOH, the extraction and stirring times, and the kind of SPME fiber used. 

The reactions were conducted according to a two factorial design with three variables, which contains experimental points at the edges and the center of a face-centered cube leading to 9 different experiments. Typically, the experiment at the center point is conducted at least 3 times to add degrees of freedom that allow the estimation of experimental error. Hence a total of 11 experiments are needed to predict the reaction rate within the parameter space. The parameter space for the catalysts to be prepared is shown in columns 2-4 in Table 1. 

In general the cube portion might be replicated times and the star portion might be replicated times. Also, it might be possible to use a fractional factorial design of resolution less than V if the experimenter is prepared to assume that certain interactions are negligible. A central composite design in four variables is shown in Table 2.6. In this table, runs 1-16 are the cube portion, runs 17-24 are the star portion, and runs 25-27 are the center points. 

In the past, the scale-up was carried out by selecting best guess process parameters. The recent trend is to employ the Factorial and Modified Factorial Designs and Search Methods. These statistically designed experimental plans can generate mathematical relationships between the independent variables, such as process factors, and dependent variables, such as product properties. This approach still requires an effective laboratory/pilot scale development program and an understanding of the variables that affect the product properties. 

The fractional factorial designs, including the Latin squares, are generally used for screening possible experimental variables in order to find which are the most important for further study. Their use is subject to some fairly severe assumptions which should be known and taken into consideration when interpreting the data ... 

The designs for this kind of experimentation can be built up similarly to the factorial designs, starting with the simple case in which only two materials are mixed together. The effective number of variables will be one less than the number of ingredients. 

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