Mixture design optimization

Keywords cosmetic, lipstick formulation, natural ingredient, mixture design, D-optimal 1.INTRODUCTION... 

The statistical mixture design for 5-components was carried out by using Design Expert, D-Optimal criterion (Version 6.10, Stat-Easy Inc., Minneapolis USA). In this study, there are restriction on the component proportions Xj that take the form of lower Lj and upper Uj constraint as Lj experimental results of the previous study [2,5]... 

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. 

Glajch, J. L., Kirkland, J. J., Squire, K. M., and Minor, J. M., Optimization of solvent strength and selectivity for reversed-phase liquid chromatography using an interactive mixture-design statistical technique, /. Chromatogr., 199, 57, 1980. 

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 ... 

Sub-problem 3M considers the mixture property constraints. The molecules from sub-problem 2M are considered in this sub-problem. The starting point is a list of promising solvents. From this list of solvents, the optimal mixture and the compositions of the constituents are identified by solving sub-problem 4M and sub-problem 5M. Since the first three sub-problems in the mixture design involves designing pure component solvents, these sub-problems are essentially the same as the first three sub-problems in single compound design. 

In some mixture design problems (such as formulations), it may not be necessary to consider processing issues and hence we would not have the process model constraints. In this case the problem becomes a simple mixing problem, which would already have been addressed by the miscibility criteria in sub-problem 4M. Hence, for these problems, we will not need sub-problem 5M. Also in some cases we might have to identify a mixture whose constituents perform different functions such as solvents and anti solvents for crystallization. In such cases we would have to formulate and solve more than one single compound design problems to identify the constituents and then solve the final two sub-problems to identify the optimal mixture. In certain cases we may not have process model constraints, however, we may still have to solve an optimization problem with other constraints, in sub-problem 4 and sub-problem 5m respectively. 

Karunanithi, A.T., Achenie, L.E.K., Gani, R., (2005). A new decomposition-based computer aided molecular/mixture design methodology for the design of optimal solvents and solvent mixtures. Ind. Eng. Chem. Res., 44(13), 4785-4797. 

Furlanetto, S., Orlandini, S., Marras, A. M., Mura, P., and Pinzauti, S. (2006). Mixture design in the optimization of a microemulsion system for the electrokinetic chromatographic determination of ketorolac and its impurities method development and validation. Electrophoresis 27, 805-818. 

J.H. de Boer, A.K. Smilde and D.A. Doombos, Introduction of a robustness coefficient in optimization Procedures Implementation in mixture design problems. Part I Theory, Chemometrics and Intelligent Laboratory Systems, 7 (1990) 223-236. 

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. 

P.M.J. Coenegracht, A.K. Smilde, H.J. Metting and D.A. Doombos, Comparison of optimization methods in reversed-phase HPLC using mixture designs and MCDM, Journal of Chromatography, 485 (1989) 195. 

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... 

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