Preliminary Experimental Design

There are many books that address experimental design and present factorial experimental design in detail (for example Design and Analysis of Experiments by Montgomery (1997) or Design of Experiments by Anderson and McLean (1974)). As engineers, we are faced quite often with the need to design a set of preliminary experiments for a process that very little or essentially no information is available. 

For example, if we have two independent variables (x, and x2) the following four (22) experiments can be readily designed  

If we have three independent variables to vary, the complete 2 factorial design corresponds to the following 8 experiments  

These designs are extremely powerful (from a statistical point of view) if we do not have a mathematical model of the system under investigation and we simply wish to establish the effect of each of these three independent variables (or their interaction) on the measured response variables. 

This is rarely the case in engineering. Most of the time we do have some form of a mathematical model (simple or complex) that has several unknown parameters that we wish to estimate. In these cases the above designs are very straightforward to implement however, the information may be inadequate if the mathematical model is nonlinear and comprised of several unknown parameters. In such cases, multilevel factorial designs (for example, 3k or 4k designs) may be more appropriate. 

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Comparative calculations of specific capacities of different filters or their specific filter areas should be made as part of the evaluation. Such calculations may be performed on the basis of experimental data obtained without using basic filtration equations. In designing a new filtration unit after equipment selection, calculations should be made to determine the specific capacity or specific filtration area. Basic filtration equations may be used for this purpose, with preliminary experimental constants evaluated. These constants contain information on the specific cake resistance and the resistance of the filter medium. 

The simplest and cheapest procedure to obtain standards is based on selective extraction followed by crystallization. A method developed to obtain lycopene from tomato residue using factorial experimental design consisted of a preliminary water removal with ethanol, followed by extraction with EtOAc and two successive crys-talhzation processes using dichloromethane and ethanol (1 4), producing lycopene crystals with 98% purity, measured by HPLC-PDA. Using this approach, bixin was extracted with EtOAc from annatto seeds that were previously washed with... 

The above experimental design constitute an excellent set of "preliminary experiments" for nonlinear models with several unknown parameters. Based on the analysis of these experiments we obtain estimates of the unknown parameters that we can use to design subsequent experiments in a rational manner taking advantage of all information gathered up to that point. 

AGIRE computer program for, 249, 79-81, 225-226 comparison to analysis based on rates, 249, 61-63 complex reactions, 249, 75-78 experimental design, 249, 84-85 inhibitor effects, 249, 71-75 potato acid phosphatase product inhibition, 249, 73-74 preliminary fitting, 249, 82-84 prephenate dehydratase product inhibition, 249, 72-73 product inhibition effects, 249, 72-73 prostate acid phosphatase phenyl phosphate hydrolysis, 249, 70 reactions with two substrates, 249, 75-77 reversible reactions, 249, 77-78 with simple Michaelian enzyme, 249, 63-71 [fitting equations, 249, 63] with slow-binding inhibitors, 249, 88 with unstable enzymes, for kinetic characterization, 249, 85-89. 

Once an experimental design is selected and the data are collected, then preliminary analyses of the data should be carried out. Some simple statistics - such as means, ranges, standard deviations, etc. - should be calculated to familiarize the researcher with the data and to serve as bases for comparison with previous research. These statistics can also be useful when graphing equations estimated later. 

Figure 4.13 Preliminary PLS model developed to seek out outlying samples using the scores plots. The scores of the most important factor (tl) are always plotted on the abscissa. Sample 4 has a different behaviour because the tail of the atomic peak had a strange elevation and this was detected on the third factor. Note that the samples show some grouping because of the experimental design used to prepare the calibration set.

This experimental design technique is widely used as a tool to verify the efficiency of several processes. In the present work, it was used for the purpose of obtaining information from the EPS production process consequently, a reduction in the variability, as well as in operational costs can be expected. The choice of the variables (factors that affect the process), as well as the superior (+), lower (-), and central (0) levels used in the design, was defined from preliminary studies that defined the parameters as the most significant for the production of EPS. The selected variables were aeration, agitation, and initial substrate concentration (see Table 1). 

In order to test the iminium-activation strategy, MacMillan first examined the capacity of various amines to enantioselectively catalyze the Diels-Alder reaction between dienes and a,/ -unsaturated aldehyde dienophiles [6]. Preliminary experimental findings and computational studies proved the importance of four objectives in the design of a broadly useful iminium-activation catalyst (1) the chiral amine should undergo efficient and reversible iminium ion formation (2) high... 

The values of k for each run are estimated from the preliminary data. For multi-step reactions, the method of Box and Lucas(2) may be used. Alternatively, we can make use of the fact that the model, its parameters, and the experimental error are "known". Then we may calculate the standard errors of In k, Sjn for any experimental design we propose. 

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