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Title
CERTIFICATE
DECLARATION
ACKNOWLEDGEMENT
CONTENTS
1 Review of literature and Introduction
1.0. Historical Review
1.0.1. Design of Experiments
1.0.2. Optimality of Block Designs
1.1. Summary of the Present Study
1.1.1. Construction of Hypercubic Designs from Symmetrical Factorial Experiments
1.1.2. Hypercubic Design and E-optimality
1.1.3. Application of Hypercubic Designs
1.1.4. λ-linked Block Designs through Non-adaptive Hypergeometric group testing designs for identifying at most two defectives and their optimalities.
2 Preliminary Concepts
2.0. Introduction
2.1 Definitions
3 Construction of Hypercubic Designs from Symmetrical Factorial Experiments
3.0. Introduction
3.1. Preliminary Results
3.2. Methods of Construction
3.3. Numerical Examples
4 Hypercubic Designs and E-optimality
4.0 Introduction
4.1. Measures of optimality
4.2. Preliminary Results
4.2.1. Optimality of Incomplete Block Designs
4.2.2. E-optimality of Block Designs
4.2.3. E-optimality of Regular Graph Designs
4.2.4 E-optimality of Cubic Designs
4.3. E-optimality of Hypercubic Designs
4.3.1. Sufficient conditions for E-optimality
4.3.1.1 Modified Results for determining egged values of C-matrices of two associate Hypercubic Designs
4.3.1.2 E-optimal criterion for Hypercubic Designs
4.3.2 Numerical Examples
4.3.3 Duals
5 Applications of Hypercubic Designs
5.0. Introduction
5.1. Construction of Semi-Regular Group Divisible Designs from Hypercubic Designs
5.2. Identifications of Confounded main effects and Interaction Effects in Symmetrical Factorial Experiments
5.2.1. Preliminary: Results
5.2.2. Procedure for Identifying Confounded main effects and Interaction effects in 2 Factorial Experiments
5.2.3. Procedure for Identifying Confounded main effects and Interaction effects in 3° Factorial Experiments
5.3. Construction of Confounded Experiments and Identification of Confounded effects using Hypercubic Design
5.3.1. 2 Factorial Experiment Confounded in 2 block sizes (r < n)
5.3.1.1 Confounding in Two Blocks
5.3.1.2 Confounding in more than Two Blocks
5.3.2. 3 Factorial Experiment Confounded in 3r Block sizes (r < n)
5.3.2.1 Confounding in Three Blocks
6 λ-linked Block Designs through non-adaptive Hypergeometric Group Testing Designs for Identifying at most Two Defectives and their Optimalities
6.0. Introduction
6.1. λ-- linked Block Design
6.2. Type - I optimality of Group Testing Designs for yr =_ 0 (mod 6) anc. V-? 2 (mod 6)
6.2.1 Type I optimality
6.3. Preliminary Results
6.3.1. Some Results related to Type I optimality
6.3.2. Examples of. - linked Block Designs
6.4. Main Results
6.4.1 Numerical Examples
6.5. Determination of Type I optimal Block Designs
A Brief summary of the investigation
List of Published Papers
Seminars Attended and Papers presented
Reference