Response mixture designs

Analyses for the Saxitoxins. Early methods for analysis of the saxitoxins evolved from those used for toxin isolation and purification. The principal landmarks in the development of preparative separation techniques for the saxitoxins were 1) the employment of carboxylate cation exchange resins by Schantz et al. (82) 2) the use of the polyacrylamide gel Bio-Gel P2 by Buckley and by Shimizu (5,78) and 3) the development by Buckley of an effective TLC system, including a new solvent mixture and a new visualization technique (83). The solvent mixture, designated by Buckley as "E", remains the best for general resolution of the saxitoxins. The visualization method, oxidation of the saxitoxins on silica gel TLC plates to fluorescent degradation products with hydrogen peroxide and heat, is an adaptation of the Bates and Rapoport fluorescence assay for saxitoxin in solution. Curiously, while peroxide oxidation in solution provides little or no response for the N-l-hydroxy saxitoxins, peroxide spray on TLC plates is a sensitive test for all saxitoxin derivatives with the C-12 gemdiol intact. 

In order to understand the relationship between the mixture component, physical properties and consumer acceptance of the lipstick, various lipstick formulations have to be produced. The physical properties of each formulation should be studied. The consumer acceptance towards the product also should be investigated. However, only a part of this work will be discussed in this paper. Here, natural waxes, oils and solvent have been used to produce natural ingredient based lipstick formulations based on the formulation suggested by the statistical mixture design. Contour plot and response surface graph were formed in order to understand the relationship between the mixture component and physical characteristic of the lipstick. 

Using experimental design such as Surface Response Method optimises the product formulation. This method is more satisfactory and effective than other methods such as classical one-at-a-time or mathematical methods because it can study many variables simultaneously with a low number of observations, saving time and costs [6]. Hence in this research, statistical experimental design or mixture design is used in this work in order to optimise the MUF resin formulation. 

The experimental designs discussed in Chapters 24-26 for optimization can be used also for finding the product composition or processing condition that is optimal in terms of sensory properties. In particular, central composite designs and mixture designs are much used. The analysis of the sensory response is usually in the form of a fully quadratic function of the experimental factors. The sensory response itself may be the mean score of a panel of trained panellists. One may consider such a trained panel as a sensitive instrument to measure the perceived intensity useful in describing the sensory characteristics of a food product. 

Techniques are presented for the analysis of mixture design responses and for the optimization of... 

The objectives of a formulator in performing a mixture design are to not only determine the component effects and blending relationships but also optimize the component levels to achieve a maximum or minimum response of a measured property. Unfortunately, the mixture design literature is sparse in references to mixture optimization. McLean and Anderson (9) in the classic flare example attempted to use Lagrange multipliers to maximize the equation describing the intensity of an ignited flare composition but obtained erroneous results. However, a secondary technique which was not discussed did produce the optimum. 

Example Optimization of an Eleven Component Glass Formulation. Piepel (6) discussed the generation and analysis of a mixture design consisting of eleven oxides used to prepare glasses for waste vitrification. Although many responses must be considered for the end use of this composition, the intent of Piepel s study was to minimize the response of leachability subject to the compositional constraints of ... 

Mixture designs are used to supply data for fitting continuous response surface models, either first-order models, such as... 

Figure 12.32 Mixture designs and fitted full second-order polynomial response surfaces. See text for details.

The results of three-component mixture designs are often presented as response surfaces over the triangular mixture space as shown in Figure 12.34. The Scheffe model parameters are seen to be equivalent to the responses at the vertexes. 

Coenegracht et al. [3] have introduced a four solvent system to compose mobile phases for the separation of the parent alkaloids in different medicinal dry plant materials, like Cinchona bark and Opium. Through the use of mixture designs and response surface modeling an optimal mobile phase was found for each type of plant material. These new mobile phases resulted in equally good or better separations than obtained by the procedures of the Pharmacopeias. Although separations were as predicted, the accuracy of the quantitative predictions needed to be improved. 

Mixture designs [13-18] are used for the optimisation of the composition of a mixture. They allow the construction of a response surface (i.e. a model) of a criterion from a relatively small number of preselected experiments. Levels of all variables cannot be chosen arbitrarily since the fractions % of the components add up to unity (for n components 0 <, < 1 + +. .. + q>= 1). Once the model function is found to be... 

Summarising, to optimise the partition coefficient P of a solute i, P, should be maximised by mixing three solvents in the correct proportions. The use of mixture design statistical techniques with the natural logarithm of the partition coefficient as response criterion is a valid way to achieve this. 

In the optimization of tablet formulations, different approaches can be used. The one variable at a time method requires many experiments and there is no guarantee that an optimal formulation is achieved. Moreover the interaction between different factors, which may influence the tablet properties, will not be detected [10]. The use of an experimental design can be helpful in the optimization of tablet formulations. Mixture designs can be used to describe the response (tablet properties) as a function of the... 

When the experimental region is not a priori known or when one is not interested in modelling the response but only in finding the optimal conditions, the simplex methodology may offer an alternative. This sequential method should not be confused with the simplex designs described in Section 6.5, which are mixture designs. 

Formulations almost invariably consist of mixtures of a drug substance and excipients. Their properties usually depend not so much on the quantity of each substance present as on their proportions. The total comes to 100%, so the number of independent variables is one less than the number of eomponents. This has the effect that the models and the designs have particular properties, and the designs described above (screening, factor studies, and response surfaces) normally cannot be used. The entire topic of mixture designs is fully described by Cornell. ... 

An alternative approach is the use of response surface or mixture designs to determine the transfer function. A schematic of a two-factor response surface design is given in Fig. 15B. This is accomplished in nine experimental runs and evaluates main effects, as well as factor interactions. If the variability of the inputs is known, then one can model the predicted... 

The experimental designs for mixture studies differ from the response surface designs discussed until now in only one important point. In a factorial design discussed in Chapter 3, we studied the influence of two factors — temperature and concentration — on reaction 3deld. Imagine that the levels of each of these factors were doubled. As a consequence, we would expect that not only the yield would be affected, but also the properties of the final product, such as, say, viscosity and optical density. 

---