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Journal Article

Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data

01 Jan 2003-Journal of the American Statistical Association (American Statistical Association)-Vol. 98, Iss: 461, pp 259
About: This article is published in Journal of the American Statistical Association.The article was published on 2003-01-01 and is currently open access. It has received 520 citations till now.
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17 May 2013
TL;DR: This research presents a novel and scalable approach called “Smartfitting” that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of designing and implementing statistical models for regression models.
Abstract: General Strategies.- Regression Models.- Classification Models.- Other Considerations.- Appendix.- References.- Indices.

3,672 citations


Cites background or methods from "Experiments with Mixtures: Designs,..."

  • ...Specific experimental designs (and linear model forms) exist for experiments that combine mixture and process variables (see Cornell (2002) for more details)....

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  • ...Specific experimental designs (and linear model forms) exist for experiments that combine mixture and process variables (see Cornell (2002) for more details). Yeh (1998) takes a different approach to modeling concrete mixture experiments....

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  • ...Yeh (2006) describes a standard type of experimental setup for this scenario called a mixture design (Cornell 2002; Myers and Montgomery 2009)....

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  • ...Yeh (2006) describes a standard type of experimental setup for this scenario called a mixture design (Cornell 2002; Myers and Montgomery 2009). Here, boundaries on the upper and lower limits on the mixture proportion for each ingredient are used to create multiple mixtures that methodically fill the space within the boundaries. For a specific type of mixture design, there is a corresponding linear regression model that is typically used to model the relationship between the ingredients and the outcome. These linear models can include interaction effects and higher-order terms for the ingredients. The ingredients used in Yeh (2006) were:...

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  • ...Specific experimental designs (and linear model forms) exist for experiments that combine mixture and process variables (see Cornell (2002) for more details). Yeh (1998) takes a different approach to modeling concrete mixture experiments. Here, separate experiments from 17 sources with common experimental factors were combined into one “meta-experiment” and the author used neural networks to create predictive models across the whole mixture space. Age was also included in the model. The public version of the data set includes 1030 data points across the different experiments, although Yeh (1998) states that some mixtures were removed from his analysis due to nonstandard conditions....

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Journal ArticleDOI
TL;DR: The impact of form diversity encompasses issues of stability and bioavailability, as well as development considerations such as process definition, formulation design, patent protection and regulatory control.

1,096 citations


Cites background from "Experiments with Mixtures: Designs,..."

  • ...Doptimal design [54,55] is an example of a DOE algorithm that can take a set of constraints, such as the ones described above, in combination with a target analytical model and determine the optimal set of experimental points to test....

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Journal ArticleDOI
TL;DR: In the proposed algorithm, a scalarization approach, termed angle-penalized distance, is adopted to balance convergence and diversity of the solutions in the high-dimensional objective space, and reference vectors are effective and cost-efficient for preference articulation, which is particularly desirable for many-objective optimization.
Abstract: In evolutionary multiobjective optimization, maintaining a good balance between convergence and diversity is particularly crucial to the performance of the evolutionary algorithms (EAs). In addition, it becomes increasingly important to incorporate user preferences because it will be less likely to achieve a representative subset of the Pareto-optimal solutions using a limited population size as the number of objectives increases. This paper proposes a reference vector-guided EA for many-objective optimization. The reference vectors can be used not only to decompose the original multiobjective optimization problem into a number of single-objective subproblems, but also to elucidate user preferences to target a preferred subset of the whole Pareto front (PF). In the proposed algorithm, a scalarization approach, termed angle-penalized distance, is adopted to balance convergence and diversity of the solutions in the high-dimensional objective space. An adaptation strategy is proposed to dynamically adjust the distribution of the reference vectors according to the scales of the objective functions. Our experimental results on a variety of benchmark test problems show that the proposed algorithm is highly competitive in comparison with five state-of-the-art EAs for many-objective optimization. In addition, we show that reference vectors are effective and cost-efficient for preference articulation, which is particularly desirable for many-objective optimization. Furthermore, a reference vector regeneration strategy is proposed for handling irregular PFs. Finally, the proposed algorithm is extended for solving constrained many-objective optimization problems.

1,020 citations


Cites methods from "Experiments with Mixtures: Designs,..."

  • ...First, a set of uniformly distributed points on a unit hyperplane are generated using the canonical simplex-lattice design method [65] { ui = ( u(1)i , u 2 i , ....

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MonographDOI
31 Jan 2003
TL;DR: This paper describes the design and analysis of experiments and the results obtained showed clear patterns in the designs and the analysis of the experiments showed clear conclusions about the aims and objectives of the study.
Abstract: Statistical design and analysis of experiments , Statistical design and analysis of experiments , کتابخانه دیجیتال جندی شاپور اهواز

813 citations

Journal ArticleDOI
TL;DR: The surface response methodologies: central composite design, Doehlert matrix and Box-Behnken design are discussed and applications of these techniques for optimization of sample preparation steps and determination of experimental conditions for chromatographic separations are presented.

535 citations