Experiment planning orthogonal

Because variables in models are often highly correlated, when experimental data are collected, the xrx matrix in Equation 2.9 can be badly conditioned (see Appendix A), and thus the estimates of the values of the coefficients in a model can have considerable associated uncertainty. The method of factorial experimental design forces the data to be orthogonal and avoids this problem. This method allows you to determine the relative importance of each input variable and thus to develop a parsimonious model, one that includes only the most important variables and effects. Factorial experiments also represent efficient experimentation. You systematically plan and conduct experiments in which all of the variables are changed simultaneously rather than one at a time, thus reducing the number of experiments needed. 

Upon completion of these experiments it became apparent that the differential pressure in the gap was a more important variable than the water repellency of the powder. Hence a 3 X 3 orthogonal set of experiments was planned, using nylon hair nets as the spacer instead of silicone-coated pumice. It was believed that this design would be more reproducible. 

When we select the good value of the dimensionless a, then the corresponding sequential plan remains orthogonal like its CFE basic plan. At the same time, if we do not have any special request concerning a sequential plan, the number of experiments to determine fundamental factors can be drastically reduced to... 

If the plan of experiments is rich (number of measurement n = w + 1, where w is the number of factors) and symmetrical (sum of the values of each independent variable, including the repeatable values during experiment, is equal to zero), and the variables themselves are orthogonal (i.e., independent), then the regression... 

S. Addelman, Orthogonal main effect plans for asymmetric factorial experiments. Technometrics, 4, 21-46 (1962). 

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