Optimal experimental design for systems involving both quantitative and qualitative factors
07 Dec 2003-Vol. 1, pp 556-564
TL;DR: In this article, the expected integrated mean squared error (EIMSE) criterion is used to construct alternative optimal experimental designs for RS metamodels with bias, which explicitly takes bias into account.
Abstract: Often 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.
Citations
More filters
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
13,333 citations
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.
107 citations
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
TL;DR: Experiments with both qualitative and quantitative factors occur frequently in practical applications as mentioned in this paper, and many construction methods for this kind of designs, such as marginally coupled designs, were proposed and experimented with.
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 p...
1 citations
Posted Content•
TL;DR: In this article, a new uniformity criterion, qualitative-quantitative discrepancy (QQD), is proposed for assessing the uniformity of designs with both qualitative and quantitative factors.
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.
References
More filters
Book•
01 Jan 1982
TL;DR: The text is designed for a one-term or two-quarter course in simulation offered in departments of industrial engineering, business, computer science and operations research.
Abstract: From the Publisher:
This second edition of Simulation Modeling and Analysis includes a chapter on "Simulation in Manufacturing Systems" and examples. The text is designed for a one-term or two-quarter course in simulation offered in departments of industrial engineering,business,computer science and operations research.
9,905 citations
TL;DR: In this article, the Response Surface Methodology (RSM) is used for scheduling and scheduling in response surface methodologies, and it is shown that it can be used in a variety of scenarios.
Abstract: (1996). Response Surface Methodology. IIE Transactions: Vol. 28, Scheduling and Logistics, pp. 1031-1032.
4,299 citations
Book•
05 Dec 2012
TL;DR: This paper presents a meta-modelling framework that automates the very labor-intensive and therefore time-heavy and expensive process of manually cataloging samples and generating random numbers.
Abstract: Introduction.- Estimating Volume and Count.- Generating Samples.- Increasing Efficiency.- Random Tours.- Designing and Analyzing Sample Paths.- Generating Pseudorandom Numbers.
2,215 citations
Book•
01 Jan 1987
TL;DR: In this paper, the authors present a methodology for estimating response surfaces that rival least squares based on the integrated mean squared error criterion analysis of multiresponse experiments with block effects mixture designs and analyses nonlinear response surface models.
Abstract: Introduction to response surface methodology matrix algebra, least squares, the analysis of variance, and principles of experimental design first-order models and designs second-order models and designs determining optimum conditions methods of estimating response surfaces that rival least squares based on the integrated mean squared error criterion analysis of multiresponse experiments response surface models with block effects mixture designs and analyses nonlinear response surface models Taguchi's robust parameter design additional topics and some directions for future research. Appendix: solutions to selected exercises.
1,480 citations
Book•
15 Jan 1952TL;DR: In this article, Monterey describes a books design and analysis of experiments, and the pronouncement as without difficulty as perspicacity of this design and analyses of experiments montgomery can be taken as skillfully as picked to act.
Abstract: Yeah, reviewing a books design and analysis of experiments montgomery could mount up your close associates listings. This is just one of the solutions for you to be successful. As understood, achievement does not suggest that you have wonderful points. Comprehending as skillfully as covenant even more than extra will have enough money each success. next-door to, the pronouncement as without difficulty as perspicacity of this design and analysis of experiments montgomery can be taken as skillfully as picked to act. Page Url
1,064 citations