The Orthogonal Arrays

Year 2002, Volume: 1 Issue: 3, 25 - 33, 16.12.2002

Hülya Bayrak , Aslıhan Alhan

Abstract

Examples are given for understandable this of subject. Moreover, some important experimental designs are given. It used properties of orthogonal arrays for these arrays of construction. Finally, it is researched other experimental designs transition from existence of orthogonal arrays. Therefore orthogonal arrays could have expanded to others experimental designs.

Keywords

Orthogonal Arrays, Projective Geometry, Hadamard Martices, Sets of Orthogonal Latin Squares

Ortogonal Düzenler

Abstract

Bu çalışmada, ortogonal düzenlerin kuruluş problemi üzerinde duruldu. Bu probleme cebirsel ve geometrik özellikler ile yaklaşıldı. Bu nedenle tüm kaynak taramaları tamamlandı ve konunun anlaşılabilmesi amacıyla örnekler verildi. Ayrıca, bazı önemli deneme düzenleri tanıtıldı. Bu düzenlerin kuruluşunda ortogonal düzenlerin özellikleri kullanıldı. Mevcut ortogonal düzenlerden diğer deneme düzenlerine geçiş yolları araştırıldı. Bunun sonucunda, ortogonal düzenlerin diğer deneme düzenlerine genişletilebileceği gösterildi.

Keywords

Ortogonal Düzenler, Projektif Geometri, Hadamard Matrisleri, Ortogonal Latin Kare Setleri

References

• BAYRAK, H. ve ALHAN, A. (2002), On Construction of 2-Symbol Orthogonal Arrays, Haccettepe Bulletin Natural Science and Engineering, Basımda.
• BAYRAK, H. ve ALHAN, A. (2002a), The Use of Orthogonal Latin Squares in the Construction of Orthogonal Arrays of Index Unity, Gazi Üniversitesi Fen-Edebiyat Fak. Fen Bilimleri Enstitüsü Dergisi, C.15, No.1, 345-349.
• BOSE, R.C. (1947), Mathematical Theory of Symmetrical Factorial Desings, Sankhya, 8, 107-166.
• BOSE, R.C. ve BUSH, K.A. (1952), Orthogonal Arrays of Strength Two and Three, Ann. Math. Stat., 23, 508-524.
• BOSE, R.C. (1961), On Some Connections Between the Design of Experiments and Information Theory, Bull. Inter. Stat. Inst. (32 Session, Tokyo, 1960), 38, 257-271.
• BOX, G. ve TYSSEDAL, J. (1996), Projective Properties of Certain Orthogonal Arrays, Biometrika. 83, 4, pp. 950-955.
• BROWNLEE, K.A. ve LORAINE, P.K. (1948), The Relationship Between Finite Groups and Completely Orthogonal Squares, Cubes and Hypercubes, Biometrika, 35, 277-282.
• BUSH, K.A. (1952), Orthogonal Arrays of Index Unity, Ann, Math., Stat 23, 426-434.
• CHAKRAVARTI, I.M. (1963), Orthogonal and Partially Balanced Arrays and Their Applications in Design of Experiments, Metrika, 7, 231-243.
• CHENG, C.S. (1995), Some Projection Properties of Orthogonal Arrays, The Annals of Statistics, Vol. 23, No. 4, 1223-1233.
• HEDAYAT, A.S. ve STUFKEN, J. (1999), Compound Orthogonal Arrays, Technometrics, Vol. 41, No. 1, 57-61.
• HOTELLING, H. (1944), Some Improvements in Weighing and Other Experimental Techniques, Ann. Math. Stat., 15, 297-306.
• KEMPTHORNE, O. (1947), A Simple Approach to Confounding and Fractional Replication in Fractional Experiments, Biometrika, 34, 255-272.
• LIN, D.K.J. ve DRAPER, N.R. (1992), Projection Properties of Plackett and Burman Designs, Technometrics, Vol. 34, No.4, 423-428.
• MOOD, A.M. (1946), On Hotelling’s Weighing Problem, Ann. Math. Stat., 17, 432-446.
• PALEY, R.E.A.C. (1933), On Orthogonal Matrices, J. Math. Phys., 12, 311-320.
• PLACKETT, R.L. ve BURMAN, J.P. (1943-1946), The Design of Optimum Multifactorial Experiments, Biometrika, 33, 305-325.
• RAGHAVARAO, D. (1971), Constructions and Combinatorial Prroblems in Design of Experiments, Originally Published, New York: Wiley.
• RAO, C.R. (1946), Hypercubes of Strength “d” Leading to Confounded Designs in Factorial Experiments, Bull. Cacutta Math. Soc., 38, 67-78.
• RAO, C.R. (1947), Mathematical Theory of Factorial Design Sankhya, Vol. 8, 107-166.
• ROSENBAUM, R.P. (1996), Some Useful Compound Dispersion Experiments in Quality Design, Technometrics, 38, 354-364.
• SEIDEN, E. (1950), A Theorem in Finite Projective Geometry and an Application to Statistics, Proc. Amer. Math. Soc., 1, 282-286.
• SEIDEN, E. (1954), On the Problem of Construction of Orthogonal Arrays, Ann. Math. Stat., 25, 151-156.
• SEIDEN, E. ve ZAMACH, R. (1966), On Orthogonal Arrays, Ann. Math. Stat., 37, 1355-1370.
• SYLVESTER, J.J. (1867), Thoughts on Inverse Orthogonal Matrices Simutaneous Sign Successions, and Tesselated Pavements in Two or More Colours, With Applications to Newton’s Rule, Ornamental Tile-Work and the Theory of Numbers, Phil. Mag., 34, 461-475.