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Author

Min-Qian Liu

Other affiliations: Tianjin University
Bio: Min-Qian Liu is an academic researcher from Nankai University. The author has contributed to research in topics: Latin hypercube sampling & Fractional factorial design. The author has an hindex of 23, co-authored 123 publications receiving 1798 citations. Previous affiliations of Min-Qian Liu include Tianjin University.


Papers
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Journal ArticleDOI
TL;DR: In this article, it is shown that uniform designs limit the effects of aliasing to yield reasonable efficiency and robustness together, while robust experimental designs guard against inaccurate estimates caused by model misspecification.
Abstract: SUMMARY When fitting a linear regression model to data, aliasing can adversely affect the estimates of the model coefficients and the decision of whether or not a term is significant. Optimal experimental designs give efficient estimators assuming that the true form of the model is known, while robust experimental designs guard against inaccurate estimates caused by model misspecification. Although it is rare for a single design to be both maximally efficient and robust, it is shown here that uniform designs limit the effects of aliasing to yield reasonable efficiency and robustness together. Aberration and resolution measure how well fractional factorial designs guard against the effects of aliasing. Here it is shown that the definitions of aberration and resolution may be generalised to other types of design using the discrepancy.

126 citations

Journal ArticleDOI
01 Dec 2003-Metrika
TL;DR: In this article, a lower bound of E(f fixme NOD676 ) was obtained for a supersaturated design, which is essentially a fractional factorial in which the number of potential effects is greater than the total number of runs, and a construction method for mixed-level supersaturated designs was proposed.
Abstract: A supersaturated design is essentially a fractional factorial in which the number of potential effects is greater than the number of runs. In this paper, E(f NOD ) criterion is employed for comparing supersaturated designs from the viewpoint of orthogonality and uniformity, and a lower bound of E(f NOD ) which can serve as a benchmark of design optimality is obtained. It is shown that the existing E(s 2) and ave χ2 criteria (for two- and three-level supersaturated designs respectively) are in fact special cases of this criterion. Furthermore, a construction method for mixed-level supersaturated designs is proposed and some properties of the resulting designs are investigated.

118 citations

Journal ArticleDOI
TL;DR: By further discriminating the pairwise correlations, efficient designs of runs from 6 to 24 are constructed and tabulated, demonstrating the effectiveness of the general algorithm of constructing E(s2) optimal supersaturated designs from cyclic BIBDs.

89 citations

Journal ArticleDOI
TL;DR: In this paper, the authors propose a method for constructing orthogonal Latin hypercube designs in which all the linear terms are orthogonality not only to each other, but also to the quadratic terms.
Abstract: SUMMARY Latin hypercube designs have found wide application. Such designs guarantee uniform samples for the marginal distribution of each input variable. We propose a method for constructing orthogonal Latin hypercube designs in which all the linear terms are orthogonal not only to each other, but also to the quadratic terms. This construction method is convenient and flexible, and the resulting designs can accommodate many more factors than can existing ones.

88 citations


Cited by
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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

13,333 citations

Journal ArticleDOI
Xinwei Deng1
TL;DR: Experimental design is reviewed here for broad classes of data collection and analysis problems, including: fractioning techniques based on orthogonal arrays, Latin hypercube designs and their variants for computer experimentation, efficient design for data mining and machine learning applications, and sequential design for active learning.
Abstract: Maximizing data information requires careful selection, termed design, of the points at which data are observed. Experimental design is reviewed here for broad classes of data collection and analysis problems, including: fractioning techniques based on orthogonal arrays, Latin hypercube designs and their variants for computer experimentation, efficient design for data mining and machine learning applications, and sequential design for active learning. © 2012 Wiley Periodicals, Inc. © 2012 Wiley Periodicals, Inc.

1,025 citations

Journal ArticleDOI
TL;DR: This work discusses the practice of problem solving, testing hypotheses about statistical parameters, calculating and interpreting confidence limits, tolerance limits and prediction limits, and setting up and interpreting control charts.
Abstract: THE best adjective to describe this work is \"sweep11 ing.\" The range of subject matter is so broad that it can almost be described as containing everything except fuzzy set theory. Included are explicit discussions of the basics of probability (relegated to an appendix); the practice of problem solving; testing hypotheses about statistical parameters; calculating and interpreting confidence limits; tolerance limits and prediction limits; setting up and interpreting control charts; design of experiments; analysis of variance; line and surface fitting; and maximum likelihood procedures. If you can think of something that is not in this list, then it probably means I have overlooked it.

309 citations

Journal ArticleDOI
TL;DR: This article categorizes, reviews, and analyzes the state-of-the-art single−/multi-response adaptive sampling approaches for global metamodeling in support of simulation-based engineering design and discusses some important issues that affect the success of an adaptive sampling approach.
Abstract: Metamodeling is becoming a rather popular means to approximate the expensive simulations in today’s complex engineering design problems since accurate metamodels can bring in a lot of benefits. The metamodel accuracy, however, heavily depends on the locations of the observed points. Adaptive sampling, as its name suggests, places more points in regions of interest by learning the information from previous data and metamodels. Consequently, compared to traditional space-filling sampling approaches, adaptive sampling has great potential to build more accurate metamodels with fewer points (simulations), thereby gaining increasing attention and interest by both practitioners and academicians in various fields. Noticing that there is a lack of reviews on adaptive sampling for global metamodeling in the literature, which is needed, this article categorizes, reviews, and analyzes the state-of-the-art single−/multi-response adaptive sampling approaches for global metamodeling in support of simulation-based engineering design. In addition, we also review and discuss some important issues that affect the success of an adaptive sampling approach as well as providing brief remarks on adaptive sampling for other purposes. Last, challenges and future research directions are provided and discussed.

276 citations