• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.143-153
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• 2002

Null designs form a vector space and there are only finite number of minimal null designs(up to scalar multiple), hence it is natural to look at the convex polytopes of minimal null designs. For example, when t = 0, k = 1, the convex polytope of minimal null designs is the polytope of roofs of type An. In this article, we look at the convex polytopes of minimal null designs and find many general properties on the vertices, edges, dimension, and some structural properties that might help to understand the structure of polytopes for big n, t through the structure of smaller n, t.

• 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.

• Journal of Korean Society for Quality Management
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• v.29 no.1
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• pp.24-40
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• 2001

Response surface designs can be classified, according to the shape of the experimental region, into spherical designs and cuboidal designs. Among the central composite design(CCD)s and the Box-Behnken design(BBD)s that are popular in practice, when the number of factors is k, spherical designs are tile CCDs with the axial value being $\sqrt{\textit{k}}$ and the BBDs, and cuboidal designs are the CCDs with the axial value being 1. With the CCDs having $\sqrt{\textit{k}}$ as the axial value, the radius of the experimental region varies with number of factors, but these designs are the 5-level designs. With the BBDs that are 3-level designs, the radius of the experimental region does not vary with the number of factors. In this article, we propose tile 3-level spherical designs which are constructed so that tile radius of the experimental region varies with the number of factors.

• 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.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.661-666
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• 2001

In this paper we consider the properties of group divisible designs and triangular designs which belong to linked block designs. These designs have minimum number of experiments among the same average efficiency factor Optimal complete diallel cross designs are constructed by these designs. A list is prepared of all linked block designs in the class of group divisible designs and triangular designs enumerated by Clatworthy(1773).

• Journal of the Korean Data and Information Science Society
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• v.1
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• pp.7-33
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• 1990

Bechhofer and Tamhane(1981) developed a theory of optimal incomplete block designs for comparing several treatments with a control. This class of designs is appropriate for comparing simultaneously $p{\geq}2$ test treatments with a control treatment (the so-called multiple comparisons with a control (MCC) problem) when the observations are taken in incomplete blocks of common size $K{\<}p+1$. In this paper we want to extend to partially BTIB designs with two associate classes for the MCC problem. We propose a new class of incomplete block designs that are partially balanced with respect to test treatments. Because the class of designs that we consider is larger than the class of designs in Bechhofer and Tamhane and provides us with designs that improve on the optimal designs in their class. We shall use the abbreviation PBTIB to refer to such designs. We study their structure and give some methods of construction. Also we describe a procedure for making exact joint confidence statements for the MCC problem in PBTIB Designs with two associate classes. We study Optimality, Admissibility considerations in PBTIB designs with two associate classes.

• Journal of the Korean Statistical Society
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• v.34 no.2
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• pp.153-160
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• 2005

In this paper, modified second order slope rotatable designs are introduced and modified slope rotatable central composite designs (SRCCD) are constructed for $2 {\le} v {\le} 17$ (v: the number of factors). Further, it can be shown for certain values of 'v', the modified SRCCD can be viewed as SRCCD constructed as with the technique of augmentation of second order rotatable design (SORD) using central composite design to SRCCD. These designs are useful in parts to estimate responses and slopes with spherical variance functions.

• 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.

• Journal of the Korean Statistical Society
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• v.11 no.1
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• pp.1-11
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• 1982

Srivastava and Anderson(1970) illustrate a method of obtaining Balanced (but not orthogonal) Resolution $IV^*$ designs starting with a BIB design. The incidence matrix of a BIB design with parameters (v, b, r, k, and $\lambda$) is utilized to obtain Balanced Resolution $IV^*$ designs with m factors and n=2b runs, where $m \leq v$. In this paper, the same idea is extended to the case of PBIB designs to obtain Partially Balanced Resolution $IV^*$ designs. In the designs obtained here the variances are balanced and the covariances are partially balanced with respect to the main effects. A proof of this property of Partially Balanced Resoultion $IV^*$ designs is given. The efficiency of Partially Balanced Resolution $IV^*$ designs is also considered and examples of Partially Balanced Resoultion $IV^*$ designs are included.

• Journal of the Korean Society of Costume
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• v.52 no.4
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• pp.125-139
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• 2002

This research was conducted to develop soccer uniform designs for the enforcement of the identity of Korea. Throughout the development of the image of Taeguek and the pattern of tiger on the soccer uniform design, it was tried to show colors and symbolic elements representing Korean traditional themes. The contents of the research cover; first, analysis of historic changes in Korean uniform design for the representative soccer players and uniform designs of the soccer players in other countries; second, analysis of the image of Taeguek and the pattern of tiger; third, analysis of the surveys of professional soccer players; and forth, uniform designs proposed and evaluation. To develope new uniform designs, Taeguek and tiger motives were adopted to express the identity of Korea by looking at the analysis of uniforms in countries including Korea. In an addition, today's fashion trends of active sportswear were analyzed to get the new idea of design. With considering the surveys of the professional soccer players in Korea, the functional designs identifying the Korean image could have come out. As a results of this research new designs of national soccer players' uniform including 4 designs for the motif of Taeguek, 4 designs for the motif of guae, 4 designs for colors of Taeguek, 4 designs for the motif of Tiger were developed, and 2 samples were made. Surveys for evaluation comparing new design & present uniform were progressed. An aesthetic and symbolic aspects of new design were better than present uniform regarding this survey.