Experimental factorial

Chisholm B, Potyrailo R, Cawse J, Shaffer R, Brennan M, Molaison C, Whisenhunt D, Elanagan B, Olson D, Akhave J, Saunders D, Mehrabi A, Eicon M (2002) The development of combinatorial chemistry methods for coating development -1. Overview of the experimental factory. Prog Org Coat 45 313-321... 

Fleury used the above diagrams to explain some explosions which occurred in an experimental factory at Sevran-Livry, in September and October, 1929. 

In the experimental factory at Christiansand till the nitrite produced is made by this process. 

B. G. Klimov, ed., Opytnyi lavod Gosudarstvennogo Instituta Prikladnoi Khimii, I9I6-I926 [The Experimental Factory of the State Institute of Applied Chemistry, 1916-1926], (Leningrad, 1927), 26. 

Redmond et al. [60] gave an example of an experimental factorial design to study the infiuence of composition and process parameters on the emulsion quality. They used the cream composition given in Table 4. They also draw up a fractional factorial designed experiment contemplating the following variables (Tables 5 and 6) in order to determine whether or not a continuous making could be used ... 

Oxidation of methane to formaldehyde. One of the first studies in this area was reportedly an experimental factory production of formalin in the United States from natural gas (Empire Refining Co., 1930) with a capacity of 70 million gallons (265 million litres) of a mixture of formaldehyde, methanol, and acetaldehyde. The description of the installation and the method, as well as the yields, has not been published. However, in contrast to the oxidation of propane and butane (associated gas), the processes of direct oxidation of methane have not received widespread in the United States. Two industrial processes for production of formaldehyde from methane were developed in Germany. To produce formaldehyde, methane was oxidized with molecular oxygen in the presence of 1—2% of nitrogen oxides or a heterogeneous catalyst (94% Cu, and 6% Sn). The oxidation of methane in the presence of platinum or palladium yielded mainly formic acid. In this case, the reaction proceeds at a very high rate, so it is impossible to isolate oxidation intermediates, formaldehyde, and methanol [174]. 

A 2 factorial design with two factors requires four runs, or sets of experimental conditions, for which the uncoded levels, coded levels, and responses are shown in Table 14.4. The terms Po> Po> Pfc> and Pafc in equation 14.4 account for, respectively, the mean effect (which is the average response), first-order effects due to factors A and B, and the interaction between the two factors. Estimates for these parameters are given by the following equations... 

The following set of experiments provides practical examples of the optimization of experimental conditions. Examples include simplex optimization, factorial designs used to develop empirical models of response surfaces, and the fitting of experimental data to theoretical models of the response surface. 

Oles, P. J. Fractional Factorial Experimental Design as a Teaching Tool for Quantitative Analysis, /. Chem. Educ. 

This experiment examines the effect of reaction time, temperature, and mole ratio of reactants on the synthetic yield of acetylferrocene by a Eriedel-Crafts acylation of ferrocene. A central composite experimental design is used to find the optimum conditions, but the experiment could be modified to use a factorial design. 

An additional advantage of biU factorial and fractional factorial designs is that by providing a comprehensive scanning of the experimental region they can often identify, without any further analyses, one or two test conditions that are better than any others. The region around these conditions can then be explored further in subsequent experimentation. 

C. Daniel, App/ications of Statistics to lndustria/Experimentation, ]oE Wiley Sons, Inc., New York, 1976. This book is based on the personal experiences and insights of the author, an eminent practitioner of industrial appHcations of experimental design. It provides extensive discussions and concepts, especially in the areas of factorial and fractional factorial designs. "The book should be of use to experimenters who have some knowledge of elementary statistics and to statisticians who want simple explanations, detailed examples, and a documentation of the variety of outcomes that may be encountered." Some of the unusual features are chapters on "Sequences of fractional repHcates" and "Trend-robust plans," and sections entided, "What is the answer (what is the question )," and "Conclusions and apologies."... 

When a reaction has many participants, which may be the case even of apparently simple processes like pyrolysis of ethane or synthesis of methanol, a factorial or other experimental design can be made and the data subjected to a re.spon.se. suiface analysis (Davies, Design and Analysis of Industrial Experiments, Oliver Boyd, 1954). A quadratic of this type for the variables X, Xo, and X3 is... 

Cropley made general recommendations to develop kinetic models for compUcated rate expressions. His approach includes first formulating a hyperbolic non-linear model in dimensionless form by linear statistical methods. This way, essential terms are identified and others are rejected, to reduce the number of unknown parameters. Only toward the end when model is reduced to the essential parts is non-linear estimation of parameters involved. His ten steps are summarized below. Their basis is a set of rate data measured in a recycle reactor using a sixteen experiment fractional factorial experimental design at two levels in five variables, with additional three repeated centerpoints. To these are added two outlier... 

This brief summary is devoted to machines, not to the science they permitted. Yet, science relies critically on experimentation, the making of which may start in a laboratory, workshop, or in a factory. Astronomy is quite peculiar in respect of experimentation. It relies almost exclusively on contemplation recording images of inaccessible objects and their spectral properties i.e., recording data cubes (two angular coordinates and a spectral one), without any capability to act on the parameters of the observed object. Few sciences have lesser means to experiment yet none, perhaps, delivers so much with so little. 

As an analytical method becomes more complex, the number of factors is likely to increase and the likelihood is that the simple approach to experimental design described above will not be successful. In particular, the possibility of interaction between factors that will have an effect on the experimental outcome must be considered and factorial design [2] allows such interactions to be probed. 

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. 

Gonzalez, A. G., TWo Level Factorial Experimental Designs Based on Multiple Linear Regression Models A Tutorial Digest Illustrated by Case Studies, Analytica Chimica Acta 360, 1998, 227-241. 

The final structure of resins produced depends on the reaction condition. Formaldehyde to phenol (F/P) and hydroxyl to phenol (OH/P) molar ratios as well as ruction temperahne were the most important parameters in synthesis of resols. In this study, the effect of F/P and OH/P wt%, and reaction temperature on the chemical structure (mono-, di- and trisubstitution of methyrol group, methylene bridge, phenolic hemiformals, etc.) was studied utilizing a two-level full factorial experimental design. The result obtained may be applied to control the physical and chemical properties of pre-polymer. 

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