Construction of experimental designs

The construction of an experimental design for this separation problem is complicated because both mixture and process variables are present. The former variables, which describe the composition of a mixture in terms of fractions, usually result in design spaces which are a subspace of a simplex (e.g. of a triangle or a tetrahedron). Process variables, on the other hand, are really independent. The design space is often a square or a cube. In this paper there are four mixture variables and two process variables. The design space is therefore a part of a tetrahedron in the mixture space, and a square in the process variables space. 

Unfortunately, the design as developed could not completely be performed because of breakdown of the equipment. Therefore some experiments were performed at the temperature and relative humidity of the laboratory. The design used consists of 65 design points. 

The levels for temperature and relative humidity were not according a factorial design because of the breakdown. However, experiments for all the settings of the mixture design were performed. 

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The statistical techniques associated with response surface methodology are concerned primarily with two aspects of the experimentation process the construction of experimental designs that yield data to permit the efficient modeling of the response surfaces, and the analysis of the experimental data and derived response surfaces. 

This chapter is intended to describe the basic methods applied in the construction of experimental designs. An essential part of this chapter is the examination of a formal approach to investigating a research problem according to the black box principle and the factor spaces related to it. 

To the above we may add several other criteria (10). They are not used directly for the construction of experimental designs in the way that the D-optimal and the D-efficiency criteria are used, but they are often useful for comparison once several D-optimal solutions, of the same or different numbers of experiments, have been found. 

For each scenario, the statistical analysis of this type of experimental design would be a two-way analysis of variance. This is predicated on the construction of the experiment, which includes some implicit assumptions. These assumptions are... 

C.A.A. Duineveld, A.K. Smilde and D.A. Doombos, Comparison of experimental designs combining process and mixture variables. Part 1 Design construction and theoretical evaluation, Chemometrics and Intelligent Laboratory Systems, 19 (1993) 295-308. 

A design is constructed which covers the experimental region in a suitable manner. General rules for the construction of such designs can be found in Box and Draper [12],... 

The design of experiments (DOE) is part of response-surface modeling (RSM) methodology. The purpose of experimental designs is to deliver as much information as possible with a minimum of experimental or financial effort. This information is then employed in the construction of sensible models of the objects under investigation. 

Suppose we wish to construct an experimental design for a mixture consisting of four components and model it with a cubic polynomial model, as described by Equation 8.14. Our task is to construct a 4,3 simplex-lattice design with q = 4 and v = 3. The proportions of each of the components are calculated by Equation 8.16, giving the following values ... 

There is also a useful function called aaugment that is used to construct augmented experimental designs. The idea is similar to the approach used for the construction of... 

The authors would like to thank Dr Gareth Davies and Prof. Jim Hutchison for help with various aspects of experimental design and construction, Prof. Fredrik... 

The construction of experimental set-ups differ in the way of wave generation, wave propagation and damping detection. One of the possible designs is shown in Fig. 6.2. The capillary waves are produced by a vibrator attached to a drive unit of a loudspeaker. The wave damping is determined via a microscope and stroboscope. The set-up works in a frequency range from 25 Hz to 4 kHz. 

Definition of Experimental Design and construction of testing facilities... 

This paper explores how models may be developed to account for the relationship between the stable isotope composition of a body tissue of an organism and its diet. The main approach taken is to express this relationship as an explicit equation, or a DIFF , and then to show how the values of such a DIFF can be evaluated from published experimental data. These values can be expected to have a much wider meaning than a simple encapsulation of a particular experimental design. As a main example, we show how the values may be used to constract a metabolic model in which the synthesis of non-essential amino acid for collagen construction can be treated. A second example is to show how the evaluation, in terms of diet, of the spacing between collagen and carbonate 6 C may be put on a rigorous basis. 

For technological applications it is highly desirable to be able to design self-assembling systems to have particular physico-chemical properties under a given set of experimental conditions. Using computer simulation, it is possible to construct an atomistic model of tapes, ribbons and fibrils to study all of the interatomic interactions within the system in a quantitative manner. Figure 13 shows atomistic... 

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