• Journal of the Korean Statistical Society
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• 제14권1호
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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.

• 한국신뢰성학회:학술대회논문집
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• 한국신뢰성학회 2002년도 정기학술대회
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• pp.411-414
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• 2002

A class of block designs for general combining ability comparisons within two groups of inbred lines in diallel crosses is given. Use is made of balanced block designs obtained by cyclically developing a single initial block.

• Journal of the Korean Data and Information Science Society
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• 제13권2호
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• pp.175-184
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• 2002

In this paper, diallel crosses block designs for control versus test comparisons among the lines are proposed. These block designs are constructed by using partially balanced incomplete block designs with C-properties. Also, the efficiencies of the diallel crosses block designs obtained through this method are tabulated for number of lines 22 or less.

• Communications for Statistical Applications and Methods
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• 제9권1호
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• pp.53-61
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• 2002

In this paper we proposed the method of the block designs for diallel crosses when inbred lines are divided into two groups. These block designs are derived by using kornecker product designs with two balanced incomplete block designs, and their efficiency factor evaluated. A table of diallel crosses for up to p$_1$$\leq$15 lines, p$_2$$\leq$15 lines in each set is also provided.

• 응용통계연구
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• 제3권2호
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• pp.55-77
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• 1990

지금까지의 단일 block size를 전제로 한 E-optimal block design들을 다수 block size로 확 장하는 문제를 종합 정리하고(Lee & Jacroux(1987) 참조), 이를 토대로 기존의 단일 block size를 갖는 block design의 table들을 이용하여 여러 block size의 종류들 중에서 우선 실용 도가 가장 높은 경우인 두 가지 상이한 block size를 갖는 새로운 E-optimal block design의 table을 제작하였음.

• 응용통계연구
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• 제24권4호
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• pp.647-656
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• 2011

발생행렬은 블완비블럭계획법을 나타내는 좋은 도구이나 우리가 발생행렬을 이용하여 관심의 대상인 블완비블럭계획법이 균형불완비블럭계획법이 되는 지를 알기는 충분하지 않다. 그래서 필요한 수단이 구조행렬이다. 불완비블럭계획법을 평가하기 위한 또 다른 수단으로서 우리는 확장발생행렬과 ${\lambda}$행렬을 제안할 수 있다. 확장발생행렬과 ${\lambda}$행렬을 통하여 우리는 관심의 대상인 블완비블럭계획법이 균형불완비블럭계획법이 되는 지를 명확히 밝힐 수가 있고, 그 패턴도 상세히 파악할 수 있게 된다.

• Communications for Statistical Applications and Methods
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• 제12권1호
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• pp.181-189
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• 2005

This paper suggest a method of inclusion probability proportional to size sampling that provides a non-negative and stable variance estimator. The sampling procedure is quite simple and flexible since a sampling design is easily obtained using mathematical programming. This scheme appears to be preferable to Nigam, Kumar and Gupta's (1984) method which uses a balanced incomplete block designs. A comparison is made with their method through an example in the literature.

• Communications for Statistical Applications and Methods
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• 제11권1호
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• pp.169-179
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• 2004

Partially balanced diallel cross designs with m-associate classes are defined and two general methods of construction are presented. Two-associate class designs based upon group divisible, triangular, and extended group divisible association schemes obtained using the general methods are also given. Tables of designs for p$\leq$24 are also provided.

• Journal of the Korean Statistical Society
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• 제3권2호
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• pp.85-101
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• 1974

In a Balanced Factorial Experiments (BFE) with n factors $F_1, F_2,\cdots,F_n$ at $m_1, m_2,\cdots,m_n$ levels respectively, Shah [15] has considered the following association scheme: the two treatments are the $(P_1, P_2,\cdot,P_n)$th associates, where $p_i=1$ if the ith factor occurs at the same level in both treatments and $p_i=0$ otherwise; $\lambda_{(p_1,p_2,\cdots,p_n)}$ will denote the number of times these treatments occur together in a block. He has showed that a BFE is partially Blanced Incomplete Block(PBIB) design with repsect to the above association scheme. Kurjian and Zelan [6] have proved that factorial designs possessing a Property A (a particular structure for their matrix NN') are factorially balanced.

• Journal of the Korean Statistical Society
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• 제15권2호
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• pp.118-126
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• 1986

The relationships between combined estimators and generalized least squares estimators in block designs are reviewed. Here combined estimators mean the best linear combination of intrablock and interblock estimaters. It is well known that only for balanced incomplete block designs the combined estimators of Yates and of the generalized least squares estimators give the same result. In this paper, a general form of the combined estimators for treatment effects is derived and it can be seen that such estimators are equivalent to the generalized least squares estimators.