- Response surface methodology
Response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. The method was introduced by G. E. P. Box and
K. B. Wilsonin 1951. The main idea of RSM is to use a set of designed experiments to obtain an optimal response. Box and Wilson suggest using a first-degree polynomialmodel to do this. They acknowledge that this model is only an approximation, but use it because such a model is easy to estimate and apply, even when little is known about the process.
An easy way to estimate a first-degree polynomial model is to use a
factorial experimentor a fractional factorial designs. This is sufficient to determine which explanatory variables have an impact on 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 designcan 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) a response.
Some extensions of response surface methodology deal with the multiple response problem. Multiple response variables create difficulty because what is optimal for one response may not be very optimal for other responses. Other extensions are used to reduce variability in a single response while targeting a specific value, or attaining a near maximum or minimum while preventing variability in that response from getting too large.
Significant criticisms of RSM include the fact that the optimization is almost always done with a model for which the coefficients are estimated, not known. That is, an optimum value may only look optimal, but be far from the truth because of variability in the coefficients. A
contour plotis frequently used to find the responses of two variables to find these coefficients by including a large number of trials in each and combinations of them, and using some sort of interpolation to find potentially better intermediate values between them. But since experimental runs often cost a lot of time and money, it can also be difficult to pinpoint the ideal coefficients, as well; there are frequently strategies used to find those values with minimal runs. Experimental designs used in RSM must make tradeoffs between reducing variability and reducing the negative impact that can be caused by bias.
*Box, G. E. P. and Wilson, K.B. (1951) On the Experimental Attainment of Optimum Conditions (with discussion). "
Journal of the Royal Statistical Society" Series B 13(1):1-45.
* [http://sumo.intec.ugent.be/?q=SUMO_toolbox Matlab SUrrogate MOdeling Toolbox - SUMO Toolbox] - Matlab code for Response Surface Modeling
Wikimedia Foundation. 2010.
Look at other dictionaries:
Mean and predicted response — In linear regression mean response and predicted response are values of the dependent variable calculated from the regression parameters and a given value of the independent variable. The values of these two responses are the same, but their… … Wikipedia
Descartes: methodology — Stephen Gaukroger INTRODUCTION The seventeenth century is often referred to as the century of the Scientific Revolution, a time of fundamental scientific change in which traditional theories were either replaced by new ones or radically… … History of philosophy
Auditory brainstem response — The auditory brainstem response (ABR) is an auditory evoked potential extracted from ongoing electrical activity in the brain and recorded via electrodes placed on the scalp. The resulting recording is a series of vertex positive waves of which I … Wikipedia
International response to the War in Darfur — While there is a general consensus in the international community that ethnic groups have been targeted and that crimes against humanity have therefore occurred, there has been debate in some quarters about whether genocide has taken place. In… … Wikipedia
Optimal design — This article is about the topic in the design of experiments. For the topic in optimal control theory, see shape optimization. Gustav Elfving developed the optimal design of experiments, and so minimized surveyors need for theodolite measurements … Wikipedia
Ergonomics — Ergonomics: the science of designing user interaction with equipment and workplaces to fit the user. Ergonomics is the study of designing equipment and devices that fit the human body, its movements, and its cognitive abilities. The International … Wikipedia
Multidisciplinary design optimization — Multi disciplinary design optimization (MDO) is a field of engineering that uses optimization methods to solve design problems incorporating a number of disciplines. As defined by Prof. Carlo Poloni, MDO is the art of finding the best compromise … Wikipedia
Design of experiments — In general usage, design of experiments (DOE) or experimental design is the design of any information gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms… … Wikipedia
Randomized controlled trial — Flowchart of four phases (enrollment, intervention allocation, follow up, and data analysis) of a parallel randomized trial of two groups, modified from the CONSORT (Consolidated Standards of Reporting Trials) 2010 Statement … Wikipedia
Linear regression — Example of simple linear regression, which has one independent variable In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one… … Wikipedia