In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. The method was introduced by George E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response. Box and Wilson suggest using a second-degree polynomial model to do this. They acknowledge that this model is only an approximation, but they use it because such a model is easy to estimate and apply, even when little is known about the process.
Statistical approaches such as RSM can be employed to maximize the production of a special substance by optimization of operational factors. Of late, for formulation optimization, the RSM, using proper design of experiments (DoE), has become extensively used. In contrast to conventional methods, the interaction among process variables can be determined by statistical techniques.
An easy way to estimate a first-degree polynomial model is to use a factorial experiment or a fractional factorial design. This is sufficient to determine which explanatory variables affect the response variable(s) of interest. Once it is suspected that only significant explanatory variables are left, then a more complicated design, such as a central composite design can be implemented to estimate a second-degree polynomial model, which is still only an approximation at best. However, the second-degree model can be used to optimize (maximize, minimize, or attain a specific target for) the response variable(s) of interest.
OrthogonalityThe property that allows individual effects of the k-factors to be estimated independently without (or with minimal) confounding. Also orthogonality provides minimum variance estimates of the model coefficient so that they are uncorrelated.
RotatabilityThe property of rotating points of the design about the center of the factor space. The moments of the distribution of the design points are constant.
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In the academic or industrial world, to optimize a system, it is necessary to establish strategies for the experimental approach. The DOE allows you to choose the best set of measurement points to min
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Joseph Diez Gergonne (19 June 1771 at Nancy, France – 4 May 1859 at Montpellier, France) was a French mathematician and logician. In 1791, Gergonne enlisted in the French army as a captain. That army was undergoing rapid expansion because the French government feared a foreign invasion intended to undo the French Revolution and restore Louis XVI to the throne of France. He saw action in the major battle of Valmy on 20 September 1792. He then returned to civilian life but soon was called up again and took part in the French invasion of Spain in 1794.
In the design of experiments, optimal designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith. In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design.
In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design. Such an experiment allows the investigator to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable.
Explores response surface design, emphasizing lack of fit analysis and quadratic models, with practical examples in Matlab.
Explores the construction and application of Hadamard matrices for efficient estimation of main effects without interactions in the Plackett-Burman Design.
Explores the basics of statistics, the significance of experimental designs, and their practical applications in various fields.
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SPRINGER INTERNATIONAL PUBLISHING AG2022
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