• Title/Summary/Keyword: balanced incomplete block designs

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Optimal Block Designs for Complete Diallel Cross

  • Park, Kuey-Chung;Son, Young-Nam
    • Communications for Statistical Applications and Methods
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    • v.8 no.1
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    • pp.65-71
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    • 2001
  • In this paper, optimal block designs for complete diallel crosses are proposed. These optimal block designs are constructed by using triangular partially balanced incomplete designs derived from symmetric balanced incomplete block designs. Also, it is shown that block designs for complete dialle crosses derived from complementary designs of triangular designs are optimal block designs.

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Optimal Design for Complete Diallel Crosses

  • Park, Kuey-Chung;Son, Young-Nam
    • Communications for Statistical Applications and Methods
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    • v.8 no.3
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    • pp.677-683
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    • 2001
  • In this paper, optimal block designs for complete diallel crosses are proposed. These optimal block designs for estimating general combining abilities are constructed by using balanced incomplete block designs and nested balanced incomplete block designs. Also, the efficiency of the optimal block design obtained through this method is reported in table.

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Block Designs for Partial Diallel Crosses (부분이면교배에서의 블록계획)

  • 손영남;최규정
    • The Korean Journal of Applied Statistics
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    • v.15 no.2
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    • pp.367-379
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    • 2002
  • In this paper, the method of constructing incomplete block designs for comparing general combining abilities of p inbred lines for partial diallel crosses is proposed. These partial diallel crosses block designs are constructed by using m-associate class partially balanced incomplete block designs with block size 2 and balanced incomplete block designs. Also, the efficiencies of block designs obtained through this method are tabulated for number of lines 24 or less.

Partial Diallel Crosses Designs using m-Associate Class Partially Balanced Incomplete Block Designs

  • Choi Kuey Chung;Son Young Nam
    • Proceedings of the Korean Statistical Society Conference
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    • 2001.11a
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    • pp.121-124
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    • 2001
  • In this paper, partial diallel crosses designs are proposed. These designs for estimating general combining abilities are constructed by using m-associate class partially balanced incomplete block designs. Also, the efficiency of the partially diallel crosses designs obtained through this method is reported in table.

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AN EXPLICIT FORMULA AND ITS FAST ALGORITHM FOR A CLASS OF SYMMETRIC BALANCED INCOMPLETE BLOCK DESIGNS

  • KANG SUNGKWON;LEE JU-HYUN
    • Journal of applied mathematics & informatics
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    • v.19 no.1_2
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    • pp.105-125
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    • 2005
  • Motivated by the field experimental designs in agriculture, the theory of block designs has been applied to several areas such as statistics, combinatorics, communication networks, distributed systems, cryptography, etc. An explicit formula and its fast computational algorithm for a class of symmetric balanced incomplete block designs are presented. Based on the formula and the careful investigation of the modulus multiplication table, the algorithm is developed. The computational costs of the algorithm is superior to those of the conventional ones.

R Type-S Block Designs for Control versus Test Inbred Lines Comparisons for Diallel Crosses

  • Son, Young-Nam
    • Communications for Statistical Applications and Methods
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    • v.9 no.2
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    • pp.443-450
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    • 2002
  • In this paper, block designs for control versus test comparisons among the lines for diallel crosses are proposed. These block designs are constructed by using balanced incomplete block designs. Also, the efficiencies of the diallel crosses block designs obtained through this method are tabulated for number of lines 23 or less.

Orthogonal Block Designs for Partial Diallel Crosses

  • Son, Young Nam;Choi, Kuey Chung
    • Communications for Statistical Applications and Methods
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    • v.9 no.2
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    • pp.435-441
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    • 2002
  • In this paper, orthogonal block designs for partial diallel crosses are proposed. These partial diallel crosses block designs for estimating general combining abilities are constructed by using $\alpha$-resolvable partially balanced incomplete block designs. Also, the efficiencies of the partial diallel crosses block designs obtained through this method are reported in table.

Cyclic Factorial Association Scheme Partially Balanced Incomplete Block Designs

  • Paik, U.B.
    • Journal of the Korean Statistical Society
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    • v.14 no.1
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    • pp.29-38
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    • 1985
  • Cyclic Factorial Association Scheme (CFAS) for incomplete block designs in a factorial experiment is defined. It is a generalization of EGD/($2^n-1$)-PBIB designs defined by Hinkelmann (1964) or Binary Number Association Scheme (BNAS) named by Paik and Federer (1973). A property of PBIB designs having CFAS is investigated and it is shown that the structural matrix NN' of such designs has a pattern of multi-nested block circulant matrix. The generalized inverse of (rI-NN'/k) is obtained. Generalized Cyclic incomplete block designs for factorial experiments introduced by John (1973) are presented as the examples of CFAS-PBIB designs. Finally, the relationship between CFAS and BNAS in block designs is briefly discussed.

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λ Matrix for Evaluating an Incomplete Bloc Design (불완비블록계획법을 평가하기 위한 λ행렬)

  • Jang, Dae-Heung
    • The Korean Journal of Applied Statistics
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    • v.24 no.4
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    • pp.647-656
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    • 2011
  • Incidence matrix is a useful tool for presenting incomplete block designs; however, it is inadequate to use only an incidence matrix in examining whether a certain incomplete block design becomes a balanced incomplete block design or not. We can use a structural matrix as a useful tool to show whether a certain incomplete block design becomes a balanced incomplete block design or not. We propose an augmented incidence matrix and ${\lambda}$ matrix as another tools for evaluating incomplete block designs. Through the augmented incidenc matrix and ${\lambda}$ matrix, we can ascertain whether a certain incomplete block design becomes a balance incomplete block design or not.

ON SECOND ORDER SLOPE ROTATABLE DESIGNS - A REVIEW

  • Victorbabu, B. Re.
    • Journal of the Korean Statistical Society
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    • v.36 no.3
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    • pp.373-386
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    • 2007
  • In this paper, a review on second order slope rotatable designs (SOSRD) is studied. Further, different methods of constructions of SOSRD like slope rotatable central composite designs (SRCCD), SOSRD using balanced incomplete block designs (BIBD), SOSRD using pairwise balanced designs (PBD), SOSRD using partially balanced incomplete block type designs (PBIBD) and SOSRD using symmetrical unequal block arrangements (SUBA) with two unequal block sizes are examined in detail. A table is provided where for a range of different values of v (v stands for number of factors) the design points needed by different methods are compared. The optimum SOSRD with minimum number of design points for each factor is suggested for $2{\leq}v{\leq}16$.