• Journal of applied mathematics & informatics
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• v.29 no.5_6
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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.

• Journal of Korean Society for Quality Management
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• v.45 no.4
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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.

• The Korean Journal of Applied Statistics
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• v.24 no.3
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• pp.505-513
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• 2011

Sudoku is a famous Latin-square-based number-placement puzzle. Mo and Xu (2008) proposed Sudoku square designs based on the idea of Sudoku. Using several Sudoku square designs which are mutually orthogonal, we can suggest the orthogonal Sudoku square designs with block effect discrimination.

• Journal of Korean Society for Quality Management
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• v.32 no.4
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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.

• The Korean Journal of Applied Statistics
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• v.5 no.2
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• pp.169-179
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• 1992

It is shown that a structurally complete row-column design has orthogonal factorial structure if each of its component designs has orthogonal factorial structure. It implies that such designs are most easily constructed via the amalgamating of one-dimensional block designs which have orthogonal factorial structure. However, this does not always hold for structurally incomplete row-column designs. A structurally incomplete row-column design is derived from the design with adjusted orthogonality, by simply interchanging row and treatment numbers.

• Journal of the Korean Statistical Society
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• v.34 no.2
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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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• 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.

• Journal of Korean Society for Quality Management
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• v.36 no.3
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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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• 2006.04a
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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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• v.17 no.3
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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.