Response surface methodology
01 Mar 2010-Wiley Interdisciplinary Reviews: Computational Statistics (John Wiley & Sons, Ltd)-Vol. 2, Iss: 2, pp 128-149
TL;DR: A survey of the various stages in the development of response surface methodology RSM is provided, organized in three parts that describe the evolution of RSM since its introduction in the early 1950s.
Abstract: The purpose of this article is to provide a survey of the various stages in the development of response surface methodology RSM. The coverage of these stages is organized in three parts that describe the evolution of RSM since its introduction in the early 1950s. Part I covers the period, 1951-1975, during which the so-called classical RSM was developed. This includes a review of basic experimental designs for fitting linear response surface models, in addition to a description of methods for the determination of optimum operating conditions. Part II, which covers the period, 1976-1999, discusses more recent modeling techniques in RSM, in addition to a coverage of Taguchi's robust parameter design and its response surface alternative approach. Part III provides a coverage of further extensions and research directions in modern RSM. This includes discussions concerning response surface models with random effects, generalized linear models, and graphical techniques for comparing response surface designs. Copyright © 2010 John Wiley & Sons, Inc.
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TL;DR: In this article, the authors systematically cover the significant developments of the last decade, including surrogate modeling of electrical machines and direct and stochastic search algorithms for both single and multi-objective design optimization problems.
Abstract: This paper systematically covers the significant developments of the last decade, including surrogate modeling of electrical machines and direct and stochastic search algorithms for both single- and multi-objective design optimization problems. The specific challenges and the dedicated algorithms for electric machine design are discussed, followed by benchmark studies comparing response surface (RS) and differential evolution (DE) algorithms on a permanent-magnet-synchronous-motor design with five independent variables and a strong nonlinear multiobjective Pareto front and on a function with eleven independent variables. The results show that RS and DE are comparable when the optimization employs only a small number of candidate designs and DE performs better when more candidates are considered.
264 citations
Cites methods from "Response surface methodology"
...To see the effect of a reduced number of design evaluations, RS is also carried out using a Box-Behnken (BB) [12] set of only 46 candidate...
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TL;DR: In this paper, a comparative study of the efficiency of different coagulants in textile wastewater treatment was carried out, and the results showed that the use of natural coagulate instead of synthetic ones has demonstrated significant advantages since it provides a low cost and environmentally friendly technology for removing dyes.
248 citations
TL;DR: A taxonomy that aims at giving an overview of the full spectrum of current simulation–optimization approaches is provided, which may guide researchers who want to use one of the existing methods, give insights into the cross-fertilization of the ideas applied in those methods and create a standard for a better communication in the scientific community.
218 citations
Additional excerpts
...The latter, which include the well-known Response Surface Methodology (RSM) – see [33], alternate between model construction (from simulation responses) and deterministic optimization....
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TL;DR: In this paper, the design and analysis of simulation experiments are discussed via two types of metamodel (surrogate emulator) and analysis via low-order polynomial regression and Kriging (or Gaussian process).
213 citations
TL;DR: A hybrid MCDM method combining simple additive weighting (SAW), techniques for order preference by similarity to an ideal solution (TOPSIS) and grey relational analysis (GRA) techniques, which can guide a decision maker in making a reasonable judgment without requiring professional skills or extensive experience is presented.
203 citations
Cites methods from "Response surface methodology"
...The response surface method (RSM) is a collection of mathematical techniques based on the fit of a polynomial equation to the experimental data obtained in relation to the experimental design [22]....
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References
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Book•
01 Jan 1983TL;DR: In this paper, a generalization of the analysis of variance is given for these models using log- likelihoods, illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables), and gamma (variance components).
Abstract: The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation. A generalization of the analysis of variance is given for these models using log- likelihoods. These generalized linear models are illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables) and gamma (variance components).
23,215 citations
Book•
29 Aug 1995TL;DR: Using a practical approach, this book discusses two-level factorial and fractional factorial designs, several aspects of empirical modeling with regression techniques, focusing on response surface methodology, mixture experiments and robust design techniques.
Abstract: From the Publisher:
Using a practical approach, it discusses two-level factorial and fractional factorial designs, several aspects of empirical modeling with regression techniques, focusing on response surface methodology, mixture experiments and robust design techniques. Features numerous authentic application examples and problems. Illustrates how computers can be a useful aid in problem solving. Includes a disk containing computer programs for a response surface methodology simulation exercise and concerning mixtures.
10,104 citations
01 May 1972
TL;DR: In this paper, the authors used iterative weighted linear regression to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation.
Abstract: JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Blackwell Publishing and Royal Statistical Society are collaborating with JSTOR to digitize, preserve and extend access to Journal of the Royal Statistical Society. Series A (General). SUMMARY The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation. A generalization of the analysis of variance is given for these models using log-likelihoods. These generalized linear models are illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables) and gamma (variance components). The implications of the approach in designing statistics courses are discussed.
8,793 citations
TL;DR: In this paper, a method of estimating the parameters of a set of regression equations is reported which involves application of Aitken's generalized least-squares to the whole system of equations.
Abstract: In this paper a method of estimating the parameters of a set of regression equations is reported which involves application of Aitken's generalized least-squares [1] to the whole system of equations. Under conditions generally encountered in practice, it is found that the regression coefficient estimators so obtained are at least asymptotically more efficient than those obtained by an equation-by-equation application of least squares. This gain in efficiency can be quite large if “independent” variables in different equations are not highly correlated and if disturbance terms in different equations are highly correlated. Further, tests of the hypothesis that all regression equation coefficient vectors are equal, based on “micro” and “macro” data, are described. If this hypothesis is accepted, there will be no aggregation bias. Finally, the estimation procedure and the “micro-test” for aggregation bias are applied in the analysis of annual investment data, 1935–1954, for two firms.
7,637 citations
Book•
01 Jan 1976
TL;DR: In this article, a text designed to make multivariate techniques available to behavioural, social, biological and medical students is presented, which includes an approach to multivariate inference based on the union-intersection and generalized likelihood ratio principles.
Abstract: A text designed to make multivariate techniques available to behavioural, social, biological and medical students. Special features include an approach to multivariate inference based on the union-intersection and generalized likelihood ratio principles.
5,807 citations