The family of screening designs aims for the study of the effect of two or more factors. In general factorial designs are the most efficient for this type of study. But the number of necessary tests is often too large when using factorial designs. There are other possible types of designs in order to take into account the limited number of experiments that can be carried out.
This tool integrates a large base of several hundred orthogonal design tables. Orthogonal design tables are preferred, as the ANOVA analysis will be based on a balanced design. Designs that are close to the design described by user input will be available for section without having to calculate for an optimal design. All existing orthogonal designs are available for up to 35 factors having each between 2 and 7 categories. Most common families like full factorial designs, Latin square and Placket and Burman designs are included.
If the existing orthogonal designs in the knowledge base do not satisfy your needs, it is possible to search for d-optimal designs. These designs might not be orthogonal.
Analysis of a screening design
Analysis of a screening design uses the same conceptual framework as linear regression and variance (ANOVA). The main difference comes from the nature of the underlying model. In ANOVA, explanatory variables are often called factors.
Surface response designs
The family of surface response design is used for modeling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize this response.
Remark: In contrast to this, screening designs aim to study the input factors, not the response value.
For example, suppose that an engineer wants to find the optimal levels of the pressure (x1) and the temperature (x2) of an industrial process to produce concrete, which should have a maximum hardness y.
Analysis of a surface response design
The analysis of a surface response design uses the same statistical and conceptual framework as linear regression. The main difference comes from the model that is used.
Mixture designs are used to model the results of experiments where these relate to the optimization of formulations. The resulting model is called "mixture distribution".
When the concentrations of the n components are not submitted to any constraint, the experimental design is a simplex, that is to say, a regular polyhedron with n vertices in a space of dimension n-1. For example, for a mixture of three components, the experimental field is an equilateral triangle; for 4 constituents it is a regular tetrahedron.
Creating mixture designs therefore consist of positioning regularly the experiences in the simplex to optimize the accuracy of the model. The most conventional designs are Scheffé’s designs, Scheffé-centroid designs, and augmented designs.
If constraints on the components of the model are introduced by defining a minimum amount or a maximum amount not to exceed, then, the experimental domain can be a simplex, an inverted simplex (also called simplex B) or a any convex polyhedron. In the latter case, the simplex designs are no longer usable.
Analysis of a mixture design
The analysis of a mixture design is based on the same principle as linear regression. The major difference comes from the model that is used. Several models are available.
By default, XLSTAT associates a reduced model (Simplified Canonical Model) to centroïd simplexes. However, it is possible to change the model if the number of degrees of freedom is sufficient (by increasing the number of repetitions of the experiments). Otherwise, an error message will be displayed informing you that the number of experiments is too small for all the model coefficients to be estimated.
To fulfil the constraint associated to a mixture design, a polynomial model with no intercept is used. We distinguish two types of models, simplified (special) models and full models (from level 3).
Estimation of these models is done with classical regression.
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