Fractional factorial analysis

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. 

In the case of constraints on proportions of components the approach is known, simplex-centroid designs are constructed with coded or pseudocomponents [23]. Coded factors in this case are linear functions of real component proportions, and data analysis is not much more complicated in that case. If upper and lower constraints (bounds) are placed on some of the X resulting in a factor space whose shape is different from the simplex, then the formulas for estimating the model coefficients are not easily expressible. In the simplex-centroid x 23 full factorial design or simplex-lattice x 2n design [5], the number of points increases rapidly with increasing numbers of mixture components and/or process factors. In such situations, instead of full factorial we use fractional factorial experiments. The number of experimental trials required for studying the combined effects of the mixture com-... 

To evaluate how the formulation components affect extrusion product performance, a fractional factorial design was created for statistical analysis. The fractional design is shown for the Neat and treated straw composite testing in Table 2. As already noted, Degradel and Degrade2 represent wheat straw that was inoculated with P. ostreatus and incubated for 6 and 12 wk, respectively. The values in Table 2 are percentages required to make a 2-kg batch for extrusion. 

Liao, C. T. (2000). Identification of dispersion effects from unreplicated 2n k fractional factorial designs. Computational Statistics and Data Analysis, 33, 291-298. 

Langsrud, O. and Naes, T. (1998). A unified frameworkfor significance testing in fractional factorials. Computational Statistics and Data Analysis, 28, 413—431. 

Andres, T. H. and Hajas, W.C. (1993). Using iterated fractional factorial design to screen parameters in sensitivity analysis of a probabilistic risk assessment model. Proceedings of the Joint International Conference on Mathematical Models and Supercomputing in... 

Steven Gilmour is Professor of Statistics in the School of Mathematical Sciences at Queen Mary, University of London. His interests are in the design and analysis of experiments with complex treatment structures, including supersaturated designs, fractional factorial designs, response surface methodology, nonlinear models, and random treatment effects. 

---