Browse > Article

Experimental Designs for Computer Experiments and for Industrial Experiments with Model Unknown  

Fang, Kai-Tai (Department of Mathematics, Hong Kong Baptist University)
Publication Information
Journal of the Korean Statistical Society / v.31, no.3, 2002 , pp. 277-299 More about this Journal
Abstract
Most statistical designs, such as orthogonal designs and optimal designs, are based on a specific statistical model. It is very often that the experimenter does not completely know the underlying model between the response and the factors. In computer experiments, the underlying model is known, but too complicated. In this case we can treat the model as a black box, or model to be unknown. Both cases need a space filling design. The uniform design is one of space filling designs and seeks experimental points to be uniformly scattered on the domain. The uniform design can be used for computer experiments and also for industrial experiments when the underlying model is unknown. In this paper we shall introduce the theory and method of the uniform design and related data analysis and modelling methods. Applications of the uniform design to industry and other areas are discussed.
Keywords
Computer experiments; experiment with mixtures; factorial design; uniform design;
Citations & Related Records
연도 인용수 순위
  • Reference
1 A note on uniformity and orthogonality /
[ Ma, C.X.;Fang, K.T.;Lin, D.K.J. ] / Journal of Statistical Planning Inference
2 Random Number Generation and Quasi-Monte Carlo Methods /
[ Niederreiter, H. ] / SIAM CBMS-NSF Regional Conference Series in Applied Mathematics
3 Experimental design and observation for large systems /
[ Bates, R.A.;Buck, R.J.;Riccomagnom E.;Wynn, H.P. ] / Journal of the Royal Statistical Society
4 /
[ Dey, A.;Mukerjee, R. ] / Wavelets: A Tutorial in Theory and Applications
5 Uniform design and its applications in chemistry and chemical engineering /
[ Liang, Y.Z.;Fang, K.T.;Xu, Q.S. ] / Chemometrics and Intelligent Laboratory Systems   DOI   ScienceOn
6 Number theoretic methods in applied statistics(Ⅱ) /
[ Wang, Y.;Fang, K.T. ] / Chinese Annals of Mathematics
7 Uniform coverage designs for molecule selection /
[ Lam, R.L.H.;Welch, W.J.;Young, S.S. ] / Technometrics   DOI   ScienceOn
8 Uniform shell desing /
[ Doehlert, D.H. ] / Applied Statistics   DOI   ScienceOn
9 Some applications of quasi-Monte Carlo Methods in statistics /
[ Fang, K.T.;K.T. Fang(eds.);F.J. Hickernell(eds.);H. Niederreiter(eds.) ] / In Monte Carlo and Quasi-Monte Carlo Methods 2000
10 Computer experiments /
[ Koehler, J.R.;Owen, A.B.;S. Ghosh(eds.);C.R. Rao(eds.) ] / Handbook of Statistics   DOI
11 Uniform design: Theory and applications /
[ Fang, K.T.;Lin, D.K.J.;Winker, P.;Zhang, Y. ] / Technometrics   DOI   ScienceOn
12 D-and T-optimum desings for the kinetics of a reversible chemical reaction /
[ Atkinson, A.C.;Bogacka, B.;Bogacki, M.B. ] / Chemonetrics and Intelligent laboratory Systems
13 /
[ Box, G.E.P.;Hunter, E.P.;Hunter, J.S. ] / Statistics for Experimenters
14 /
[ Cornell, J.A. ] / Experiments with Nixtures, Designs, Models, and the Analysis of Mixture Data
15 /
[ Fang, K.T.;Ma, C.X. ] / Orthogonal and Uniform Experimental Designs
16 The effects of different experimental desings on parameter estimation in the kinetics of a reversible chemical reaction /
[ Xu, Q.S.;Liang, Y.Z.;Fang, K.T. ] / Chemometrics and Intellignet Laboratory Systems   DOI   ScienceOn
17 Admissibility and minimaxity of the uniform desing in nonparametric regression model /
[ Xie, M.Y.;Fang, K.T. ] / Journal of Statistical Planning Inference   DOI   ScienceOn
18 On isomorphism of fractional factorial designs /
[ Ma, C.X.;Fang, K.T.;Lin, D.K.J. ] / Journal of Complexity   DOI   ScienceOn
19 Goodness-of-fit statistics, discrepancies and robust desings /
[ Hickernell, F.J. ] / Statistical & Probability Letters   DOI   ScienceOn
20 POlynomial splines and their tensor products in extended linear modelling /
[ Stone, C.J.;Hansen, M.H.;Kooperberg, C.;Truong, Y.K. ] / The Annals of Statistics   DOI   ScienceOn
21 /
[ Farin, G. ] / Curves and Surfaces for Computer Aided Geometric Design - A Practical Guide (3rd ed.)
22 Wrap-around L₂-discrepancy of random sampling, Latin hypercube and uniform designs /
[ Fang, K.T.;Ma, C.X. ] / Journal of Complexity   DOI   ScienceOn
23 A comparison of three methods for selecting values imput variables in the analysis of output from a computer code /
[ McKay, M.D.;Beckman, R.J.;Conover, W.J. ] / Technometrics   DOI   ScienceOn
24 A note on uniform distribution and experimental design /
[ Wang, Y.;Fang, K.T. ] / KeXue TongBao
25 /
[ Fan, J.;Gijbels, I. ] / Local Polynomial Modeling and Its Applications
26 /
[ Antoniadis, A.;Oppenheim, G. ] / Wavelets and Statistics
27 Designs for approximately linear regression: two optimality properties of uniform designs /
[ Wiens, D.P. ] / Statistics & Probability Letters   DOI   ScienceOn
28 /
[ Dey, A.;Mukerjee, R. ] / Fractional Factorial Plans
29 Model selection for analysis of uniform design and computer experiment /
[ Li, Runze;H. Pham(eds.);M.W. Lu(eds.) ] / Eight ISSAT International Conference on Reliability and Quality in Design
30 Minimum aberration <TEX>$2^{k-p}$</TEX> designs /
[ Fries, A.;Hunter, W.G. ] / Technometrics   DOI   ScienceOn
31 The uniform desing: application of number-theoretic methods in experimental design /
[ Fang, K.T. ] / Acta mathematicae Applicatae Sinica
32 The uniform design and its applications /
[ Fang, K.T.;Hickernell, F.J. ] / Bulletin of the International Statistical Institute, 50th Session, Book
33 /
[ Fang, K.T.;Wang, Y. ] / Number-theoretic Methods in Statistics
34 Sliced inverse regression for dimension reduction(with discussion) /
[ Li, K.C. ] / Journal of the American Statistical Association   DOI   ScienceOn
35 Uniform experimental desing and its application in industry /
[ Fang, K.T.;Lin, D.K.J.;C.R. Rao(ed.) ] / Handbook of Statistics: Statistics in Industry
36 Optimal U-type design /
[ Winker, P.;Fnag, K.T.;H. Niederreiter(eds.);P. Zinterhof(eds.);P. Hellekalek(eds.) ] / Monte Carlo and Quasi-Monte Carlo Methods 1996
37 Lattice rules: how well do they measure up? /
[ Hickernell, F.J.;P. Hellekalek(eds.);G. larcher(eds.) ] / Random and Quasi-Random Point Sets
38 Uniform design of experiments with mixtures /
[ Wang, Y.;Fang, K.T. ] / Science in China
39 /
[ Fang, K.T. ] / Uniform Design and Uniform Desing Tables
40 Centered L₂-discrepancy of random sampling and Latin hypercube design, and construction of uniform desing /
[ Fang, K.T.;Ma, C.X.;Winker, P. ] / Mathematics of Computation   DOI   ScienceOn
41 /
[ Caudill, M.;Butler, C. ] / Understanding Neural Networks: Computer Explorations
42 On uniform design of experiments with restricted mixtures and generation of uniform disgribution on some domains /
[ Fang, K.T.;Yang, Z.H. ] / Statistical & Probability Letters
43 Uniform designs based on Latin squares /
[ Fang, K.T.;Shiu, W.C.;Pan, J.X. ] / Statistica Sinica
44 A connection between uniformity and aberration in regular fractions of two-level factorials /
[ Fang, K.T.;Mukerjee, R. ] / Biometrika   DOI   ScienceOn