{"title":"Construction of Space-Filling Designs for Three Input Variables Computer Experiments","authors":"Kazeem A. Osuolale, Waheed B. Yahya, Babatunde L. Adeleke","volume":93,"journal":"International Journal of Computer and Information Engineering","pagesStart":1740,"pagesEnd":1745,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10001411","abstract":"Latin hypercube designs (LHDs) have been applied in\r\nmany computer experiments among the space-filling designs found in\r\nthe literature. A LHD can be randomly generated but a randomly\r\nchosen LHD may have bad properties and thus act poorly in\r\nestimation and prediction. There is a connection between Latin\r\nsquares and orthogonal arrays (OAs). A Latin square of order s\r\ninvolves an arrangement of s symbols in s rows and s columns, such\r\nthat every symbol occurs once in each row and once in each column\r\nand this exists for every non-negative integer s. In this paper, a\r\ncomputer program was written to construct orthogonal array-based\r\nLatin hypercube designs (OA-LHDs). Orthogonal arrays (OAs) were\r\nconstructed from Latin square of order s and the OAs constructed\r\nwere afterward used to construct the desired Latin hypercube designs\r\nfor three input variables for use in computer experiments. The LHDs\r\nconstructed have better space-filling properties and they can be used\r\nin computer experiments that involve only three input factors.\r\nMATLAB 2012a computer package (www.mathworks.com\/) was\r\nused for the development of the program that constructs the designs.","references":"[1] M. Bayarri, J. O. Berger, D. Higdon, M. Kennedy, A. Kottas, R. Paulo,\r\nJ. Sacks, J. Cafeo, J. Cavendish and J. Tu (2002). A Framework for the\r\nValidation of Computer Models. Proceedings of the Workshop on\r\nFoundations for V&V in the 21st Century, D. Pace and S. Stevenson,\r\neds., Society for Modelling and Simulation International.\r\n[2] R. C. Bose and K. A. Bush (1952). Orthogonal Arrays of Strength Two\r\nand Three. Annals of Mathematical Statistics 23, 508\u2013524.\r\n[3] A. S. Hedayat, N. J. A. Sloane and J. Stufken (1999). Orthogonal\r\nArrays: Theory and Applications. Springer-Verlag, New York.\r\n[4] M. Johnson, L. Moore and D. Ylvisaker (1990). Minimax and Maximin\r\nDistance Design. J. Statist. Plann. Inference 26, 131-148.\r\n[5] W. F. Kuhfeld (2009). Orthogonal Arrays. Website courtesy of SAS\r\nInstitute.\r\n[6] S. Leary, A. Bhaskar and A. Keane (2003). Optimal Orthogonal Aarray-\r\nBased Latin Hypercubes. J. Applied Statist. 30, 585-598.\r\n[7] M. D. McKay, R. J. Beckman and W. J. Conover (1979),\u201cA Comparison\r\nof Three Methods for selecting Values of Input Variables in the Analysis\r\nof Output from a Computer Code, Technometrics, 21, 239 -245.\r\n[8] R. Mukerjee and C. F. Wu (2006). A Modern Theory of Factorial\r\nDesigns. Springer Verlag.\r\n[9] K. A. Osuolale, W. B. Yahya and B. L. Adeleke (2014). An Algorithm\r\nfor constructing Space-Filling Designs for Hadamard Matrices of Orders\r\n4\u03bb and 8\u03bb. Proceedings of the 49th Annual Conference of the Science\r\nAssociation of Nigeria, 27 th April - 1st May.\r\n[10] A. B. Owen (1992a). A Central Limit Theorem for Latin Hypercube\r\nSampling, Journal of the Royal Statistical Society. B54, 541-555.\r\n[11] C. R. Rao (1946). Hypercube of Strength \u2018d\u2019 Leading to Confounded\r\nDesigns in Factorial Experiments. Bull. Calcutta Math. Soc., 38, 67-78.\r\n[12] C. R. Rao (1947). Factorial Experiments Derivable from Combinatorial\r\nArrangements of Arrays. Journal of the Royal Statistical Society\r\n(Suppl.). 9, 128-139.\r\n[13] S. Strogatz (2003). The Real Scientific Hero of 1953, New York Times.\r\nMarch 4, Editorial\/Op-Ed.\r\n[14] B. Tang (1991). Orthogonal Array-Based Latin Hypercubes. IIQP\r\nResearch Report, RR-91-10.\r\n[15] B. Tang (1993). Orthogonal Array-Based Latin Hypercubes. Journal of\r\nthe American Statistical Association 88, 1392\u20131397.\r\n[16] B. Tang (1994). A Theorem for selecting OA-Based Latin Hypercubes\r\nusing a Distance Criterion. Comm. Statist. : A Theory and Methods 23,\r\n2047-2058.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 93, 2014"}