Factorial design systematic effects

If systematic errors due to drift are expected then one can perform the design in a well defined randomized way so that the calculated main effects are not biased by the drift [36]. These designs are called anti-drift designs and they are described for full and fractional factorial designs. However, the interactions effects calculated from these designs are still biased by the drift. 

For a two-level factorial design, only two excipients can be selected for each factor. However, for the filler-binder, a combination of brittle and plastic materials is preferred for optimum compaction properties. Therefore, different combinations such as lactose with MCC or mannitol with starch can count as a single factor. Experimental responses can be powder blend flowability, compactibility, blend uniformity, uniformity of dose unit, dissolution, disintegration, and stability under stressed storage conditions. The major advantage of using a DOE to screen prototype formulations is that it allows evaluation of all potential factors simultaneously, systematically, and efficiently. It helps the scientist understand the effect of each formulation factor on each response, as well as potential interaction between factors. It also helps the scientist identify the critical factors based on statistical analysis. DOE results can define a prototype formulation that will meet the predefined requirements for product performance stability and manufacturing. 

The approach in material development is to systematically perform statistically designed experiments. Techniques include fractional factorial designs, Grecko-Latin squares, and self-directed optimization. Data collected is statistically evaluated to determine primary and combined effects of the... 

Example 1 is a two-level factorial design, with two levels of catalyst concentration, and is half-factorial that is, half of the possible combinations are omitted in a systematic manner. It can only show linear contrasts as the level of each factor is changed. It wUl allow calculation of main factor effects cleanly, but possible interactions wUl be confused with each other mathematically (referred to aliasing ). Sometimes, with half-factorials the interactions can stiU be extracted and understood. 

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. 

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