25-fractional factorial

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

This experiment describes the use of a fractional factorial design to examine the effects of volume of HNO3, molarity of AgN03, volume of AgN03, digestion temperature, and composition of wash water on the gravimetric analysis for chloride. 

This experiment describes a fractional factorial design used to examine the effects of flame height, flame stoichiometry, acetic acid, lamp current, wavelength, and slit width on the flame atomic absorbance obtained using a solution of 2.00-ppm Ag+. 

After the preceding considerations have been taken into account, a test plan is developed to best meet the goals of the program. This might involve one of the standard plans developed by statisticians. Such plans are described in various texts (Table 1) and are considered only briefly here. Sometimes, combinations of plans are encountered, such as a factorial experiment conducted in blocks or a central composite design using a fractional factorial base. 

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."... 

O. L. Davies and co-workers. The Design andAna/ysis of Industria/Experiments, 2nd ed., Hafner, New York, 1956 reprinted by Longman, New York, 1987. This book, which is a sequel to the authors basic text Statistica/Methods in Eesearch and Production, is directed at industrial situations and chemical appHcations. Three chapters are devoted to factorial experiments and one chapter to fractional factorial plans. A lengthy chapter (84 pp.) discusses the deterrnination of optimum conditions and response surface designs, which are associated with the name of G. Box, one of the seven co-authors. Theoretical material is presented in chapter appendices. 

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... 

For the PS case, a three-variable Box-Behnken response surface methodology (RSM) design using formulation variables has been carried out. For the RF system, an eight-variable fractional-factorial screening study was done first to select significant factors, and this was followed by two RSM s which were similar in design to the one done for PS. The results have led directly to substantial improvements in both materials. 

Table 2. Fractional-factorial screening design for RF foams...

As an example, a seven factor quarter fraction factorial design would be written as seen in equation below... 

Because the experimental expenditure increases strongly with the increasing number of influence factors, fractional factorial design FFD (partial factorial design) is applied in such cases. It is not possible to evaluate all the interactions by FFDs but only the main effects. 

Fractional factorial design is especially useful in case of a high number of influence variables from which the insignificant one have to be screened. 

Two Experimental versus control subjects One-at-a-time designs Factorial designs Fractional factorial designs Nested designs Special designs... 

A fractional factorial design was used to examine the effects of 9 variables which were thought to be... 

Fractional distillation of crude pine oil, 24 510 of crude sulfate turpentine, 24 476 Fractional extraction, 10 745, 759-760 Fractional factorial designs, 8 396 amount of coverage in experimental design texts compared, 8 395t commercial experimental design software compared, 8 398t Fractional velocity plots, 10 319-321 Fractionating towers, in plant layout,... 

For the complete vapor-phase oxidation of methane over a palladium alumina catalyst, conversion-space-time data were taken at 350°C and 1 atm total pressure the fractional factorial design of Table X (Hll) specified the settings of the feed partial pressures of the reacting species. 

Determination of Ibuprofen, Pseudoephedrine HCI, Chlorpheniramine Maleate and Nipagen by Liquid Chromatography and Fractional Factorial Design... 

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