Factorial design formulation

Designed experimentation, involving mostly some type or modification of factorial design, has been used to study many different types of formulation problems. These include a pharmaceutical suspension [21], a controlled-release tablet formulation [22], and a tabletcoating operation [23]. In the latter case, Dincer and Ozdurmus studied an enteric film coating and utilized the steepest descent graphic method to select the optimum. 

At this time in the investigation, the discovery was made that incorporation of a different hydrocarbon monomer at modest levels improved Property E of these copolymers. Thus, another designed experiment was necessary to determine the optimal formulation. He decided to return to the factorial design because we wanted to reexamine the effects of SiUMA chain length in combination with Variable IV. The design is set out in Table VII. 

In the following discussion, we shall again separate the terms of a hyperbolic model and identify two parameters Cl and C2. As before, each of these two parameters will be a collection of terms, one of which is multiplied by conversion and one not multiplied by conversion. In previous formulations, however, we have oriented the discussion toward a familiar type of experimental design in kinetics conversion versus space-time data at several pressure levels. Consequently, the parameters Cx and C2 were defined to exploit this data feature. Another type of design that is becoming more common is a factorial design in the feed-component partial pressures. 

As an example of the use of a Latin square as a fractional factorial design, suppose we want to find out the effect of increasing concentrations of a chemical added to retain gloss in an industrial paint formulation. The model is... 

The use of factorial and fractional factorial designs in split-plot arrangements has been investigated by Addelman [46], see also Daniel [47]. As an example of such an arrangement, consider a tablet formulation experiment with two environmental variables, temperature (T) and humidity (H), and five design variables. A, B, C, D, and E with all of the... 

A 20 run 2 fractional factorial design with four replicate center points was carried out to assess whether it was possible to optimize the current formulation for scale-up or if major reformation would be necessary. Table 3 lists the formulation variables that were evaluated. 

Statistical optimization of a controlled release formulation obtained by a double-compression process Application of a Hadamard matrix and a factorial design... 

From a minimum number of experiments, the Hadamard matrix gives the possibility of estimating the mean effects of four parameters. Among them, the particle size range had the most important effect in the release of diclofenac sodium. By interpreting data, a factorial design including only two parameters was applied from which an optimum formulation was found. 

El-Banna HM, Ismail AA, Gadalla MAF. Factorial design of experiment for stability studies in the development of a tablet formulation. Pharmazie 1984 39 163-165. 

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. 

Mixture designs are applied in cases where the levels of individual components in a formulation require optimization, but where the system is constrained by a maximum value for the overall formulation. In other words, a mixture design is often considered at this stage when the quantities of the factors must add to a fixed total. In a mixture experiment, the factors are proportions of different components of a blend. Mixture designs allow for the specification of constraints on each of the factors, such as a maximum and/or minimum value for each component, as well as for the sum and/or ratio of two or more of the factors. These designs are very specific in nature and are tied to the specific constraints that are unique to the particular formulation. However, as with the discussion of the fractional factorial designs, in order to be most efficient, it is important to provide realistic prior expectations on anticipated effects so the smallest design can be set up to fit the simplest realistic model to the data. 

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. 

It should be noted that there is a great deal of information hidden in large factorial designs n = 16). When analysis shows that only a few factors are significant, the residuals (differences between calculated and measured values) may be analyzed.A small spread of residuals under certain conditions as opposed to others may indicates better reproducibility of the process or formulation under these conditions. An example of its pharmaceutical use is presented in the example of Menon et al. l... 

The first term is known as the sum of squares, model (SSM). The second term is known as the sum of squares, residual (SSR), and the final term is known as the sum of squares, total (SST). Equation 3.16 is true for any least squares solution whatsoever. However, SSM can be apporhoned by component (i.e., Uq, a-, U2,. ..) only for so-called orthogonal models or data sets—that is, those that generate diagonal X X matrices (as is the case for factorial designs). Equation 3.16 also has a matrix formulation ... 

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