Factorial design, orthogonal

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

With simple, symmetrical, orthogonal designs like the full factorial designs, when all of the experiments have been done exactly the same number of times, then the factor effects can be calculated using simple algebra. 

Notice that this is an orthogonal design in coded factor space (-1 and +1) any one column multiplied by any other column will give a vector product of zero. Other saturated fractional factorial designs may be found in the literature [Box and Hunter (1961a, 1961b), Anderson and McLean (1974), Barker (1985), Bayne and Rubin (1986), Wheeler (1989), Diamond (1989)]. 

The highest (iBu)2NH yield (72 %) was obtained a conversion level of 92% and at reaction parameters P=13 bar, T=240°C, WHSV=1.0 g/g h, NH3/iBuOH= 1.7, H2/NH3= 1.9. In conclusion, a secondary amine yield above 70 % can be was obtained in fixed bed reactor using vanadium promoted Raney nickel catalyst without recycling unconverted alcohol. In order to describe the conversion of alcohol, as well as the yield and selectivity of diisobutylamine in the function process parameters, experiments were carried out and results were evaluated according to orthogonal factorial design (6,7). 

The philosophy is simple make products with build-in robustness against all kinds of environmental disturbances and fluctuations. The experimental design methods are presented as linear graphs and orthogonal arrays, but are not essentially different from established designs like Factorial and Fractional Factorial designs [12]. The methods of analyzing... 

The analysis of variance lends itself best to balanced factorial designs, whether complete, partially replicated, or otherwise modified. The concept of balance simplifies the calculations tremendously. There are ways of coping with missing data, unequal replication under various conditions, and even some lack of orthogonality in the design, but these methods seem to involve more calculation than the data may deserve. The analysis of variance is a procedure which makes it possible to compare the effects of the variables being studied, first independently of the effects of all other variables, and second in all possible combinations with one another. Sometimes the effect of a variable within a given level of another variable... 

Table 1 displays an orthogonal array of strength three because it contains each of the 23 = 8 level combinations of any set of three factors exactly twice. In other words, its projection onto any set of three factors consists of two replicates of the complete 23 factorial design. 

Fractional factorial designs are constructed from the model matrix X of a 2k p complete factorial design using the orthogonal columns of X to define the variable settings in 2k p experiments. 

The first term is known as the sum of squares, model (SSM). The second term is known as the sum of squares, residual (SSR), and the final term is known as the sum of squares, total (SST). Equation 3.16 is true for any least squares solution whatsoever. However, SSM can be apporhoned by component (i.e., Uq, a-, U2,. ..) only for so-called orthogonal models or data sets—that is, those that generate diagonal X X matrices (as is the case for factorial designs). Equation 3.16 also has a matrix formulation ... 

Make the design strictly orthogonal by choosing a = yjyjnnf -n II., where n is the total number of points in the design, and is the number of factorial design points. 

With respect to the second step, as the PPs are orthogonal to each other they are particularly suitable-as design variables and the simplest design strategies, like the Factorial designs, can be applied thereafter on using PPs. 

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