Screening full-factorial design

For a partial separation situation after screening, the organic modifier content and temperature are decreased according to a 2 full factorial design. When baseline separation is obtained, the retention factor can be further optimized by changing the... 

In this chapter we explore factorial-based experimental designs in more detail. We will show how these designs can be used in their full factorial form how factorial designs can be taken apart into blocks to minimize the effect of (or, if desired, to estimate the effect of) an additional factor and how only a portion of the full factorial design (a fractional replicate) can be used to screen many potentially useful factors in a very small number of experiments. Finally, we will illustrate the use of a Latin square design, a special type of fractionalized design. 

Full factorial designs at two levels are mainly used for screening, that is, to determine the influence of a number of effects on a response, and to eliminate those that are not significant, the next stage being to undertake a more detailed study. Sometimes, where detailed predictions are not required, the information from factorial designs is adequate, at least in situations where the aim is fairly qualitative (e.g. to improve the yield of a reaction rather than obtain a highly accurate rate dependence that is then interpreted in fundamental molecular terms). 

As for full factorial designs the levels of the variables are situated at the borders of the experimental interval for that variable. It is possible that the response function of that variable is curved with an optimum at an intermediate factor level (see Fig. 6.11). The effect calculated from the design can then be small and the variable may be incorrectly considered as non-significant 45. When such intermediate optima are considered possible, a solution can be to perform the screening at three levels by reflecting a... 

To build a resolution III design, first write out the effect matrix associated with the full factorial design whose size (i.e., number of runs) is just greater than the number of factors to be screened. Then assign each screening factor to a... 

Consider the screening problem of table 2.20. Here we want to know the effect of various diluents, disintegrants, lubricants etc. on the stability of the drug substance. We have not imposed any restraint whatsoever on the numbers of levels for each variable. We could of course test all possible combinations with the full factorial design, which consists of 384 experiments (4 x 2 x 3 x 4 x 2 x 2) Reference to the general additive screening model for different numbers of levels will show that the model contains 12 independent terms. Therefore the minimum number of experiments needed is also 12. 

Two-Level Designs Screening Designs Full Factorial Designs... 

Although it is not difficult to perform a screening experiment for two factors, in realistic cases it is more likely that there will be many more factors for example, if we want to screen for six factors, 2 or 64 experiments are required. The extra experiments are mainly used to study what are called the interaction terms. For example, a two-factor full factorial design at two levels requires 2 or four experiments. These experiments can be used to obtain a model between the response and the level of the factors often expressed in the form... 

Suppose that you are looking for the composition of a catalyst in terms of support, active material, and promoter. A catalyst screening test for a combination of all parameters may require a large number of expensive experimentation and a large number of samples. Instead, factoring out these three independent parameters in 2 full factorial design (Table E7.1.1) will enable you to determine the focal point of the optimum composition. The measured variable is the reaction rate. Careful measures should be taken to determine the reaction rate free from artifacts which will be explained in the later sections of this chapter. 

The essence of good planning is to design an experiment so that it is able to provide exactly the type of information sought. To do this, one must define the aim of such trials and thus choose the most suitable technique. At first, in a situation of lack of knowledge about the system to be studied, one must make a screening of the variables that exist in this system the most advisable would be to conduct experiments to follow a full factorial design [21]. 

Initial screens can be distinguished between methods that are used to determine what factors are most important, and follow-up screens that allow optimization and improvement of crystal quality (Table 14.1). In experimental design, this is known as the Box-Wilson strategy (Box et al., 1978). The first group of screens is generally based on a so-called factorial plan which determines the polynomial coefficients of a function with k variables (factors) fitted to the response surface. It can be shown that the number of necessary experiments n increases with 2 if all interactions are taken into account. Instead of running an unrealistic, large number of initial experiments, the full factorial matrix can... 

Assume that twelve factors, Xx to X12, should be screened. The random balance matrix will consist of two independent semi-replicas of a 26 full factorial experiment, with rows or design points that are randomly distributed. The 32 design points thus synthesized will start with the values taken from a normal population with the mean 100 and the standard deviation 60=2.0. The effects of factors have been introduced in the way that the following values were added to the best values of selected factors in the upper level (+) value -15 added to factor X7 value -12 added to factor X4 value +10 added to factor X10 and Xn value +8 added to factor X value +6 added to factor X5 and Xg value +4 added to factor X2 value -4 added to factor X9... 

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