Fractional-factorial designs

The residuals for this case are shown in Fig. 4.4. It can be seen that they are more or less normally distributed. Furthermore, since the reduced model has an = 0.970 with all significant parameter values, it can be concluded that the results are probably good. 

The solution to this problem using Excel is presented in Sect. 8.7.3 Factorial Design Examples. 

For a large number of factors, it may be inconvenient to perform all the necessary experiments to determine a full fractional experiment, for example, for a 10-factor experiment, a total of 2 = 1,024 experiments need to be run. Since in many cases, a single experiment can take a few hours to run, then it could easily take more than two months to complete the experiment. At the same time, it may be known that many of the higher-order interactirms may be negligible and can, thus, be ignored. This assumption is necessary, since by performing fewer experiments, some of the 

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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+. 

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."... 

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... 

Keywords Chlorpheniramine, fractional factorial design, RP-HPLC, ibuprofen, nipagen, pseudoephedrine... 

Chemometric techniques have been frequently used for optimization of analytical methods, as they are faster, more economical and effective and allow more than one variable to be optimized simultaneously. Among these, two level fractional factorial design (2 ) is used mainly for preliminary evaluation of the significance of the variables and its interactions [1]. 

The aim of this work, to develop a RP-HPLC method for the detemtination of four components given above in a new symp preparation by optimizing the experimental conditions using two level fractional factorial design. 

Nipagen by Liquid Chromatography and Fractional Factorial Design... 

Application of 2 fractional factorial design allowed the optimization of the gradient HPLC proeednie for the determination of ibnprofen, pseudoephedrine HCl, ehlor-pheniramine maleate and nipagen in symp preparation. The optimum eonditions for this determination were found to be 3 of pH, 1.5 mL/min of flow rate, 85%, 55% and 40% of buffer eompositions of steps of gradient profde. 

Abstract A preconcentration method using Amberlite XAD-16 column for the enrichment of aluminum was proposed. The optimization process was carried out using fractional factorial design. The factors involved were pH, resin amount, reagent/metal mole ratio, elution volume and samphng flow rate. The absorbance was used as analytical response. Using the optimised experimental conditions, the proposed procedure allowed determination of aluminum with a detection limit (3o/s) of 6.1 ig L and a quantification limit (lOa/s) of 20.2 pg L, and a precision which was calculated as relative standard deviation (RSD) of 2.4% for aluminum concentration of 30 pg L . The preconcentration factor of 100 was obtained. These results demonstrated that this procedure could be applied for separation and preconcentration of aluminum in the presence of several matrix. 

In this work, a procedure for the preconcentration and determination of aluminum was proposed. The experimental conditions of the procedure were obtained by using two level fractional factorial design... 

Keywords Fractional factorial design, aluminum, morin, preconcentration, XAD-16, AAS. 

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