Orthogonal array

About: Orthogonal array is a research topic. Over the lifetime, 3455 publications have been published within this topic receiving 62971 citations.

CRC Handbook of Combinatorial Designs

Abstract: Balanced Incomplete Block Designs and t-Designs2-(v,k,l) Designs of Small OrderBIBDs with Small Block Sizet-Designs, t = 3Steiner SystemsSymmetric DesignsResolvable and Near Resolvable DesignsLatin Squares, MOLS, and Orthogonal ArraysLatin SquaresMutually Orthogonal Latin Squares (MOLS)Incomplete MOLSOrthogonal Arrays of Index More Than OneOrthogonal Arrays of Strength More Than TwoPairwise Balanced DesignsPBDs and GDDs: The BasicsPBDs: Recursive ConstructionsPBD-ClosurePairwise Balanced Designs as Linear SpacesPBDs and GDDs of Higher IndexPBDs, Frames, and ResolvabilityOther Combinatorial DesignsAssociation SchemesBalanced (Part) Ternary DesignsBalanced Tournament DesignsBhaskar Rao DesignsComplete Mappings and Sequencings of Finite GroupsConfigurationsCostas ArraysCoveringsCycle SystemsDifference FamiliesDifference MatricesDifference Sets: AbelianDifference Sets: NonabelianDifference Triangle SetsDirected DesignsD-Optimal MatricesEmbedding Partial QuasigroupsEquidistant Permutation ArraysFactorial DesignsFrequency SquaresGeneralized QuadranglesGraph Decompositions and DesignsGraphical DesignsHadamard Matrices and DesignsHall Triple SystemsHowell DesignsMaximal Sets of MOLSMendelsohn DesignsThe Oberwolfach ProblemOrdered Designs and Perpendicular ArraysOrthogonal DesignsOrthogonal Main Effect PlansPackingsPartial GeometriesPartially Balanced Incomplete Block DesignsQuasigroupsQuasi-Symmetric Designs(r,l)-DesignsRoom SquaresSelf-Orthogonal Latin Squares (SOLS)SOLS with a Symmetric Orthogonal Mate (SOLSSOM)Sequences with Zero AutocorrelationSkolem SequencesSpherical t-DesignsStartersTrades and Defining Sets(t,m,s)-NetsTuscan Squarest-Wise Balanced DesignsUniformly Resolvable DesignsVector Space DesignsWeighing Matrices and Conference MatricesWhist TournamentsYouden Designs, GeneralizedYouden SquaresApplicationsCodesComputer Science: Selected ApplicationsApplications of Designs to CryptographyDerandomizationOptimality and Efficiency: Comparing Block DesignsGroup TestingScheduling a TournamentWinning the LotteryRelated Mathematics and Computational MethodsFinite Groups and DesignsNumber Theory and Finite FieldsGraphs and MultigraphsFactorizations of GraphsStrongly Regular GraphsTwo-GraphsClassical GeometriesProjective Planes, NondesarguesianComputational Methods in Design TheoryIndex

Fundamental Concepts In The Design of Experiments

Abstract: 1. The Experiment, the Design, and the Analysis 1.1 Introduction 1.2 The Experiment 1.3 The Design 1.4 The Analysis 1.5 Examples 1.6 Summary in Outline Further Reading Problems 2. Review of Statistical Inference 2.1 Introduction 2.2 Estimation 2.3 Tests of hypothesis 2.4 The Operating Characterisitc Curve 2.5 How Large a Sample? 2.6 Application to Tests on Variances 2.7 Application to Tests on Means 2.8 Assessing Normality 2.9 Applications to Tests on Proportions 2.10 Analysis of Experiments with SAS Further Reading Problems 3. Single-Factor Experiments with No Restrictions on Randomization 3.1 Introduction 3.2 Analysis of Variance Rationale 3.3 After ANOVA-What? 3.4 Tests of Means 3.5 Confidence Limits on Means 3.6 Components of Variance 3.7 Checking the Model 3.8 SAS Programs for ANOVA and Tests after ANOVA 3.9 Summary Further Reading Problems 4. Single-Factor Experiments -- Randomized Block and Latin Square Designs 4.1 Introduction 4.2 Randomized Complete Block Design 4.3 ANOVA Rationale 4.4 Missing Values 4.5 Latin Squares 4.6 Interpretations 4.7 Assessing the Model 4.8 Graeco-Latin Squares 4.9 Extensions 4.10 SAS Programs for Randomized Blocks and Latin Squares 4.11 Summary Further Reading Problems 5. Factorial Experiments 5.1 Introduction 5.2 Factorial Experiments: An Example 5.3 Interpretations 5.4 The Model and Its Assessment 5.5 ANOVA Rationale 5.6 One Observation Per Treatment 5.7 SAS Programs for Factorial Experiments 5.8 Summary Further Reading Summary 6. Fixed, Random, and Mixed Models 6.1 Introduction 6.2 Single-Factor Models 6.3 Two-Factor Models 6.4 EMS Rule 6.5 EMS Derivations 6.6 The Pseudo-F Test 6.7 Expected Mean Squares Via Statistical Computing Packages 6.8 Remarks 6.9 Repeatability and Reproducibility for a Measurement System Further Reading Problems 7. Nested and Nested-Factorial Experiments 7.1 Introduction 7.2 Nested Experiments 7.3 ANOVA Rationale 7.4 Nested-Factorial Experiments 7.5 Repeated-Measures Design and Nested-Factorial Experiments 7.6 SAS Programs for Nested and Nested-Factorial Experiments 7.7 Summary Further Reading Problems 8. Experiments of Two or More Factors -- Restrictions and Randomization 8.1 Introductin 8.2 Factorial Experiment in a Randomized Block Design 8.3 Factorial Experiment in a Latin Square Design 8.4 Remarks 8.5 SAS Programs 8.6 Summary Further Reading Problems 9.2 2 Squared Factorial 9.3 2 Cubed Factorial 9.4 2f Factorial 9.5 The Yates Method 9.6 Analysis of 2f Factorials When n=1 9.8 Summary Further Reading Problems 10. 3f Factorial Experiments 10.1 Introduction 10.2 3 Squared Factorial 10.3 3 Cubed Factorial 10.4 Computer Programs 10.5 Summary Further Reading Problems 11. Factorial Experiment -- Split-Plot Design 11.1 Introduction 11.2 A Split-Plot Design 11.3 A Split-Split-Plot Design 11.4 Using SAS to Analyze a Split-Plot Experiment 11.5 Summary Further Reading Problems 12. Factorial Experiment -- Confounding in Blocks 12.1 Introduction 12.2 Confounding Systems 12.3 Block Confounding -- No Replication 12.4 Blcok Confounding with Replication 12.5 Confounding in 3F Factorials 12.6 SAS Progrms 12.7 Summary Further Reading Problems 13. Fractional Replication 13.1 Introduction 13.2 Aliases 13.3 2f Fractional Replication 13.4 Plackett-Burman Designs 14. Taguchi Approach to the Design of Experiments 14.1 Introduction 14.2 The L4 (2 Cubed) Orthogonal Array 14.3 Outer Arrays 14.4 Signal-To-Noise-Ratio 14.5 The L8 (2 7) Orthogonal Array 14.6 The L16 (2 15) Orthogonal Array 14.7 The L9 (3 4) Orthogonal Array 14.8 Some Other Taguchi Designs 14.9 Summary Futher Reading Problems 15. Regression 15.1 Introduction 15.2 Linear Regression 15.3 Curvilinear Regression 15.4 Orthogronal Polynomials 15.5 Multiple Regression 15.6 Summary Further Reading Summary 16. Miscellaneous Topics 16.1 Introduction 16.2 Covariance Analysis 16.3 Response-Surface Experimentation 16.4 Evolutionary Operation (EVOP) 16.5 Analysis of Attribute Data 16.6 Randomized Incomplete Blocks -- Restriction On Experimentation 16.7 Youden Squares Further Reading Problems SUMMARY AND SPECIAL PROBLEMS GLOSSARY OF TERMS REFERENCES STATISTICAL TABLES Table A Areas Under the Normal Curve Table B Student's t Distribution Table C Cumulative Chi-Square Distribution Table D Cumulative F Distribution Table E.1 Upper 5 Percent of Studentized Range q Table E.2 Upper 1 Percent of Studentized Range q Table F Coefficients of Orthogonal Polynomials ANSWERS TO SELECTED PROBLEMS INDEX

Orthogonal Arrays: Theory and Applications

Abstract: 1 Introduction.- 1.1 Problems.- 2 Rao's Inequalities and Improvements.- 2.1 Introduction.- 2.2 Rao's Inequalities.- 2.3 Improvements on Rao's Bounds for Strength 2 and 3.- 2.4 Improvements on Rao's Bounds for Arrays of Index Unity.- 2.5 Orthogonal Arrays with Two Levels.- 2.6 Concluding Remarks.- 2.7 Notes on Chapter 2.- 2.8 Problems.- 3 Orthogonal Arrays and Galois Fields.- 3.1 Introduction.- 3.2 Bush's Construction.- 3.3 Addelman and Kempthorne's Construction.- 3.4 The Rao-Hamming Construction.- 3.5 Conditions for a Matrix.- 3.6 Concluding Remarks.- 3.7 Problems.- 4 Orthogonal Arrays and Error-Correcting Codes.- 4.1 An Introduction to Error-Correcting Codes.- 4.2 Linear Codes.- 4.3 Linear Codes and Linear Orthogonal Arrays.- 4.4 Weight Enumerators and Delsarte's Theorem.- 4.5 The Linear Programming Bound.- 4.6 Concluding Remarks.- 4.7 Notes on Chapter 4.- 4.8 Problems.- 5 Construction of Orthogonal Arrays from Codes.- 5.1 Extending a Code by Adding More Coordinates.- 5.2 Cyclic Codes.- 5.3 The Rao-Hamming Construction Revisited.- 5.4 BCH Codes.- 5.5 Reed-Solomon Codes.- 5.6 MDS Codes and Orthogonal Arrays of Index Unity.- 5.7 Quadratic Residue and Golay Codes.- 5.8 Reed-Muller Codes.- 5.9 Codes from Finite Geometries.- 5.10 Nordstrom-Robinson and Related Codes.- 5.11 Examples of Binary Codes and Orthogonal Arrays.- 5.12 Examples of Ternary Codes and Orthogonal Arrays.- 5.13 Examples of Quaternary Codes and Orthogonal Arrays.- 5.14 Notes on Chapter 5.- 5.15 Problems.- 6 Orthogonal Arrays and Difference Schemes.- 6.1 Difference Schemes.- 6.2 Orthogonal Arrays Via Difference Schemes.- 6.3 Bose and Bush's Recursive Construction.- 6.4 Difference Schemes of Index 2.- 6.5 Generalizations and Variations.- 6.6 Concluding Remarks.- 6.7 Notes on Chapter 6.- 6.8 Problems.- 7 Orthogonal Arrays and Hadamard Matrices.- 7.1 Introduction.- 7.2 Basic Properties of Hadamard Matrices.- 7.3 The Connection Between Hadamard Matrices and Orthogonal Arrays.- 7.4 Constructions for Hadamard Matrices.- 7.5 Hadamard Matrices of Orders up to 200.- 7.6 Notes on Chapter 7.- 7.7 Problems.- 8 Orthogonal Arrays and Latin Squares.- 8.1 Latin Squares and Orthogonal Latin Squares.- 8.2 Frequency Squares and Orthogonal Frequency Squares.- 8.3 Orthogonal Arrays from Pairwise Orthogonal Latin Squares.- 8.4 Concluding Remarks.- 8.5 Problems.- 9 Mixed Orthogonal Arrays.- 9.1 Introduction.- 9.2 The Rao Inequalities for Mixed Orthogonal Arrays.- 9.3 Constructing Mixed Orthogonal Arrays.- 9.4 Further Constructions.- 9.5 Notes on Chapter 9.- 9.6 Problems.- 10 Further Constructions and Related Structures.- 10.1 Constructions Inspired by Coding Theory.- 10.2 The Juxtaposition Construction.- 10.3 The (u, u + ?) Construction.- 10.4 Construction X4.- 10.5 Orthogonal Arrays from Union of Translates of a Linear Code.- 10.6 Bounds on Large Orthogonal Arrays.- 10.7 Compound Orthogonal Arrays.- 10.8 Orthogonal Multi-Arrays.- 10.9 Transversal Designs, Resilient Functions and Nets.- 10.10 Schematic Orthogonal Arrays.- 10.11 Problems.- 11 Statistical Application of Orthogonal Arrays.- 11.1 Factorial Experiments.- 11.2 Notation and Terminology.- 11.3 Factorial Effects.- 11.4 Analysis of Experiments Based on Orthogonal Arrays.- 11.5 Two-Level Fractional Factorials with a Defining Relation.- 11.6 Blocking for a 2k-n Fractional Factorial.- 11.7 Orthogonal Main-Effects Plans and Orthogonal Arrays.- 11.8 Robust Design.- 11.9 Other Types of Designs.- 11.10 Notes on Chapter 11.- 11.11 Problems.- 12 Tables of Orthogonal Arrays.- 12.1 Tables of Orthogonal Arrays of Minimal Index.- 12.2 Description of Tables 12.1?12.3.- 12.3 Index Tables.- 12.4 If No Suitable Orthogonal Array Is Available.- 12.5 Connections with Other Structures.- 12.6 Other Tables.- Appendix A: Galois Fields.- A.1 Definition of a Field.- A.2 The Construction of Galois Fields.- A.3 The Existence of Galois Fields.- A.4 Quadratic Residues in Galois Fields.- A.5 Problems.- Author Index.

Experimental design

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.