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Proceedings ArticleDOI

Optimal experimental design for systems involving both quantitative and qualitative factors

Chantarat1, Ning Zheng1, Allen1, Deng Huang1 
07 Dec 2003-Vol. 1, pp 556-564

AbstractOften in discrete-event simulation, factors being considered are qualitative such as machine type, production method, job release policy, and factory layout type. It is also often of interest to create a response surface (RS) metamodel for visualization of input-output relationships. Several methods have been proposed in the literature for RS metamodeling with qualitative factors but the resulting metamodels may be expected to predict poorly because of sensitivity to misspecification or bias. This paper proposes the use of the expected integrated mean squared error (EIMSE) criterion to construct alternative optimal experimental designs. This approach explicitly takes bias into account. We use a discrete-event simulation example from the literature, coded in ARENA/spl trade/, to illustrate the proposed method and to compare metamodeling accuracy of alternative approaches computationally.

Topics: Metamodeling (56%), Mean squared error (51%)

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Citations
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Journal Article
TL;DR: This book by a teacher of statistics (as well as a consultant for "experimenters") is a comprehensive study of the philosophical background for the statistical design of experiment.
Abstract: THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

12,326 citations


Journal ArticleDOI
TL;DR: A class of three-level response surface designs is introduced which allows all except the quadratic parameters to be estimated orthogonally, as well as having a number of other useful properties.
Abstract: Many processes in the biological industries are studied using response surface methodology. The use of biological materials, however, means that run-to-run variation is typically much greater than that in many experiments in mechanical or chemical engineering and so the designs used require greater replication. The data analysis which is performed may involve some variable selection, as well as fitting polynomial response surface models. This implies that designs should allow the parameters of the model to be estimated nearly orthogonally. A class of three-level response surface designs is introduced which allows all except the quadratic parameters to be estimated orthogonally, as well as having a number of other useful properties. These subset designs are obtained by using two-level factorial designs in subsets of the factors, with the other factors being held at their middle level. This allows their properties to be easily explored. Replacing some of the two-level designs with fractional replicates broadens the class of useful designs, especially with five or more factors, and sometimes incomplete subsets can be used. It is very simple to include a few two- and four-level factors in these designs by excluding subsets with these factors at the middle level. Subset designs can be easily modified to include factors with five or more levels by allowing a different pair of levels to be used in different subsets.

100 citations


Journal ArticleDOI
TL;DR: New designs are proposed specifically to address bias and compared with five types of alternatives ranging from types of composite to D-optimal designs using four criteria including D-efficiency and measured accuracy on test problems.
Abstract: This paper explores the issue of model misspecification, or bias, in the context of response surface design problems involving quantitative and qualitative factors. New designs are proposed specifically to address bias and compared with five types of alternatives ranging from types of composite to D-optimal designs using four criteria including D-efficiency and measured accuracy on test problems. Findings include that certain designs from the literature are expected to cause prediction errors that practitioners would likely find unacceptable. A case study relating to the selection of science, technology, engineering, or mathematics majors by college students confirms that the expected substantial improvements in prediction accuracy using the proposed designs can be realized in relevant situations. Copyright © 2011 John Wiley & Sons, Ltd.

8 citations


Posted Content
Abstract: Experiments with both qualitative and quantitative factors occur frequently in practical applications. Many construction methods for this kind of designs, such as marginally coupled designs, were proposed to pursue some good space-filling structures. However, few criteria can be adapted to quantify the space-filling property of designs involving both qualitative and quantitative factors. As the uniformity is an important space-filling property of a design, in this paper, a new uniformity criterion, qualitative-quantitative discrepancy (QQD), is proposed for assessing the uniformity of designs with both types of factors. The closed form and lower bounds of the QQD are presented to calculate the exact QQD values of designs and recognize the uniform designs directly. In addition, a connection between the QQD and the balance pattern is derived, which not only helps to obtain a new lower bound but also provides a statistical justification of the QQD. Several examples show that the proposed criterion is reasonable and useful since it can distinguish distinct designs very well.

Patent
07 Nov 2008
Abstract: A method for determining, for each of at least p physical parameters of one or several components of an electronic circuit or of a microelectromechanical system, a number n of experiment values of the physical parameter includes determining n vectors of dimension p, each component of each of the vectors corresponding to one of n initial values of one of physical parameters; and iteratively modifying at least some of the n vectors to bring to a maximum, at least locally, for each pair of vectors from among pairs of n vectors, the smallest average of the sum of distances between the vectors of said pair projected onto sub-spaces of dimension k, where k belongs to a set of integers ranging between 1 and p and at least comprising 1, 2, and p, the components of each of the n vectors corresponding, at the end of the iterations, to experiment values.

References
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