• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1571-1581
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• 2011

In this paper, we construct inequivalent Hadamard matrices based on several new and old full orthogonal designs, using circulant and symmetric block matrices. Not all orthogonal designs produce inequivalent Hadamard matrices, because the corresponding systems of equations do not possess solutions. The systems of equations arising when we search for inequivalent Hadamard matrices from full orthogonal designs using circulant and symmetric block matrices, can be concisely described using the periodic autocorrelation function of the generators of the block matrices. We use Maple, Magma, C and Unix tools to find many new inequivalent Hadamard matrices.

• 품질경영학회지
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• 제45권4호
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• pp.889-902
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• 2017

Purpose: The orthogonality and trace optimal properties are desirable for constructing designs of experiments. This article focuses on the determination of the sizes of experiments for the balanced trace optimal resolution-V fractional factorial designs for 2-level factorial designs, which have near-orthogonal properties. Methods: In this paper, first we introduce the trace optimal $2^t$ fractional factorial designs for $4{\leq}t{\leq}7$, by exploiting the partially balanced array for various cases of experimental sizes. Moreover some orthogonality criteria are also suggested with which the degree of the orthogonality of the designs can be evaluated. And we appraise the orthogonal properties of the introduced designs from various aspects. Results: We evaluate the orthogonal properties for the various experimental sizes of the balanced trace optimal resolution-V fractional factorial designs of the 2-level factorials in which each factor has two levels. And the near-orthogonal 2-level balanced trace optimal resolution-V fractional factorial designs are suggested, which have adequate sizes of experiments. Conclusion: We can construct the trace optimal $2^t$ fractional factorial designs for $4{\leq}t{\leq}7$ by exploiting the results suggested in this paper, which have near-orthogonal property and appropriate experimental sizes. The suggested designs can be employed usefully especially when we intend to analyze both the main effects and two factor interactions of the 2-level factorial experiments.

• 응용통계연구
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• 제24권3호
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• pp.505-513
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• 2011

스도쿠는 라틴방격법를 기반으로하는 숫자퍼즐로서 전세계적으로 인기있는 숫자퍼즐이다. Mo와 Xu (2008)는 이 스도쿠의 개념을 이용하여 블럭효과를 구별할 수 있는 스도쿠방격법을 제안하였다. 서로 직교하고 블럭효과를 구별할 수 있는 스도쿠방격법들을 이용하면 우리는 블럭효과를 구별할 수 있는 직교스도쿠방격법을 제안할 수 있다.

• 품질경영학회지
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• 제32권4호
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• pp.220-228
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• 2004

The orthogonality is an important property in the experimental designs. When we use nearly orthogonal arrays, we need evaluate the degree of the orthogonality of given experimental designs. Graphical methods for evaluating the degree of the orthogonality of nearly orthogonal arrays are suggested.

• 응용통계연구
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• 제5권2호
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• pp.169-179
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• 1992

블록 계획에서 요인의 효과를 독립적으로 추정 할 수 있도록 그 효과를 직교되게 구성 했을 때 그 계획을 직교 요인 계획이라 한다. 빈 칸이 없는 요인 행-열 계획의 성분계획들이 직 교된 요인의 성질을 지니면 그 행-열 계획 또한 직교된 요인의 성질이 유지 된다는 사실이 입증되었다. 이러한 이유로 빈 칸이 없는 직교요인 행-열 계획은 직교된 성질을 가지는 일 차원 성분 계획들을 단순히 결합함으로써 만들 수 있다. 그러나, 이러한 관계는 빈 칸이 있 는 요인 행-열 계획에서는 성립되지 않는다. 빈칸이 있는 요인 행-열 계획의 연구는 근래에 와서 그 필요성으로 활발히 진행되고 있다. 본 논문에서는 직교된 요인의 성질을 갖는 빈 칸이 있는 요인 행-열 계획의 일부를 조정 직교된 행-열 계획에서 행과 처리를 바꿈으로 설계해 보았다.

• Journal of the Korean Statistical Society
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• 제34권2호
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• pp.141-151
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• 2005

Under the assumption that the three-level factors are quantitative, the linear effects are taken more attention than the quadratic effects of the interaction terms. Webb (1971) presented some small incomplete factorial designs that are mixed two- and three-level designs with 20 or fewer runs. The designs provided the estimating linear-by-linear components of interactions between the three-level factors; moreover, they could also offer estimation of interactions that interest the experiments. Webb used ad hoc methods to find these plans; hence, there was still no unified structure to those experiments. In this paper, we develop the methods to construct the $2^{n}3^3$ and $2^{1}3^3$ designs. The designs constructed by these methods not only supply orthogonal estimates of all the main effects but also permit estimation of all the two-factor interactions not involving the quadratic effects. Furthermore, the designs we find are nearly orthogonal.

• Communications for Statistical Applications and Methods
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• 제9권2호
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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.

• 품질경영학회지
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• 제36권3호
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• pp.13-21
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• 2008

The orthogonality is an important property in the experimental designs. When we use nearly orthogonal arrays(for example, supersaturated designs), we need evaluate the degree of the orthogonality of given nearly orthogonal arrays. We can use the mutual information as a new criterion for evaluating and testing the degree of the orthogonality of given nearly orthogonal arrays.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2006년도 PROCEEDINGS OF JOINT CONFERENCEOF KDISS AND KDAS
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• pp.49-54
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• 2006

When using response surface designs, the experimental trials should be carried out in blocks in case of heterogeneity of conditions. When we use nearly orthogonal blocking, we need evaluate the degree of orthogonal blocking. Graphical methods for evaluating the degree of orthogonal blocking are suggested.

• Journal of the Korean Data and Information Science Society
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• 제17권3호
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• pp.669-675
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• 2006

When using response surface designs, the experimental trials should be carried out in blocks in case of heterogeneity of conditions. When we use nearly orthogonal blocking, we need evaluate the degree of orthogonal blocking. Graphical methods for evaluating the degree of orthogonal blocking are suggested.