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NTIS 바로가기Applied stochastic models in business and industry, v.29 no.4, 2013년, pp.350 - 361
Pistone, Giovanni (de Castro Statistics Initiative, Collegio Carlo Alberto, Moncalieri, Italy) , Vicario, Grazia (Dipartimento di Scienze Matematiche, Politecnico di Torino, Italy)
In the production process of silicon wafers, which are crystalline slices used as substrate of electronic micro‐circuits, the thickness of the SiO2 deposition on their top is a main characteristic to be controlled during the process. The experimental design that is commonly used to monitor the thickness to the target value consists of a regular array of points lying on concentric circles, the silicon wafer itself being a disk. To speed up the control process, the engineers aim to use just only a limited subset of such points. To reconstruct the values on untried locations of the silicon wafer, the Kriging interpolation has been proposed because of its recognized ability in providing fairly good predictions. In this paper, we consider two methodological issues related to universal Kriging models. First, we discuss the modeling of the covariance structure among the measured points; in fact, spatial data usually show a strong correlation when they come from spatially near observed points. Second, we put forward an algebraic method to assess the identifiability of trend models, based both on the full experimental design and on special fractions of it. Our findings are illustrated by a data set from an industrial application. Copyright © 2013 John Wiley & Sons, Ltd.
Borgoni R , Radaelli L , Tritto V , Zappa D . Optimal reduction of a spatial monitoring grid: proposal and applications in process control . Computational Statistic and Data Analysis 2013 ; 58 : 407 – 419 .
di Bucchianico A , Janssen BJ . Linear models, Zernike polynomials and applications to wafer data . ENBIS‐11 Coimbra 4–8 September 2011 2011 .
Krige DG . A statistical approach to some basic mine valuation problems on the witwatersrand . Journal of the Chemical, Metalic and Mining Society of South Africa 1951 ; 52 ( 6 ): 119 – 139 .
Matheron G . The Theory of Regionalized Variables and its Applications . Ecole nationale superieure des mines : Paris , 1971 .
Cressie NAC . Statistics for spatial data, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics . John Wiley & Sons Inc. : New York , 1993 . Revised reprint of the 1991 edition, A Wiley‐Interscience Publication.
Cressie NAC . Spatial prediction and ordinary Kriging . Mathematical Geology 1997 ; 20 ( 4 ): 407 – 421 .
Goovaerts P . Geostatistics for Natural Resources Evaluation . Oxford University Press : New York , 1997 .
Sacks J , Welch WJ , Mitchell TJ , Wynn HP . Design and analysis of computer experiments (with discussion) . Statistical Science 1989 ; 4 : 409 – 435 .
Sacks J , Schiller SB , William J . Welch, designs for computer experiments . Technometrics 1989 ; 31 ( 1 ): 41 – 47 .
Pedone P , Vicario G , Romano D . Kriging‐based sequential inspection plans for coordinate measuring machines . Applied Stochastic Models in Business and Industry 2009 ; 25 : 133 – 149 .
Furrer R , Nychka D , Sain S . Fields: tools for spatial data, 2011, v. 6.6.1 . Available at: http://www.image.ucar.edu/Software/Fields [Accessed on Dec 2011].
Berg C , Christensen JPR , Ressel P . Harmonic Analysis on Semigroups. Theory of Positive Definite and Related Functions , Graduate Texts in Mathematics, Vol. 100 . Springer‐Verlag : New York , 1984 .
Santner TJ , Williams BJ , Notz WI . The Design and Analysis of Computer Experiments , Springer Series in Statistics. Springer‐Verlag : New York , 2003 .
R Development Core Team . R: A Language and Environment for Statistical Computing . R Foundation for Statistical Computing : Vienna, Austria , 2008 . http://www.R‐project.org.
Roustant O , Ginsbourger D , Deville Y . DiceKriging, DiceOptim: two R packages for the analysis of computer experiments by Kriging‐based metamodeling and optimization . Journal of Statistical Software 2012 ; 51 ( 1 ): 1 – 55 .
Pistone G , Riccomagno E , Wynn HP . Algebraic Statistics: Computational Commutative Algebra in Statistics , Monographs on Statistics and Applied Probability, Vol. 89 . Chapman & Hall/CRC : Boca Raton, FL , 2001 .
Gibilisco P , Riccomagno E , Rogantin MP , Wynn HP . (eds.), Algebraic and Geometric Methods in Statistics . Cambridge University Press : Cambridge , 2010 .
Cox D , Little J , O'Shea D . Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra , second ed. Undergraduate Texts in Mathematics, Springer‐Verlag : New York , 1997 .
CoCoATeam . CoCoA: a system for doing Computations in Commutative Algebra . Available at: http://cocoa.dima.unige.it [Accessed on Dec 2011], online.
Zernike F . Beugungstheorie des Schneidenver‐Fahrens und Seiner Verbesserten Form, der Phasenkontrastmethode . Physica 1 1934 ; 1 : 689 – 704 .
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