• Journal of Korean Society for Quality Management
• /
• v.45 no.4
• /
• pp.889-902
• /
• 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.

• Communications for Statistical Applications and Methods
• /
• v.16 no.1
• /
• pp.195-208
• /
• 2009

A conventional single design optimality criterion has been used to select an efficient experimental design. But, since an experimental design is constructed with respect to an optimality criterion pre specified by investigators, an experimental design obtained from one optimality criterion which is superior to other designs may perform poorly when the design is evaluated by another optimality criterion. In other words, none of these is entirely satisfactory and even there is no guarantee that a design which is constructed from using a certain design optimality criterion is also optimal to the other design optimality criteria. Thus, it is necessary to develop certain special types of experimental designs that satisfy multiple design optimality criteria simultaneously because these multi-optimal designs (MODs) reflect the needs of the experimenters more adequately. In this article, we present a heuristic approach to construct second-order response surface designs which are more flexible and potentially very useful than the designs generated from a single design optimality criterion in many real experimental situations when several competing design optimality criteria are of interest. In this paper, over cuboidal design region for $3\;{\leq}\;k\;{\leq}\;5$ variables, we construct multi-optimal designs (MODs) that might moderately satisfy two famous alphabetic design optimality criteria, G- and IV-optimality criteria using a GA which considers a certain amount of randomness. The minimum, average and maximum scaled prediction variances for the generated response surface designs are provided. Based on the average and maximum scaled prediction variances for k = 3, 4 and 5 design variables, the MODs from a genetic algorithm (GA) have better statistical property than does the theoretically optimal designs and the MODs are more flexible and useful than single-criterion optimal designs.

• Proceedings of the Korean Statistical Society Conference
• /
• 2002.05a
• /
• pp.171-174
• /
• 2002

In this paper, diallel crosses block designs for control versus test comparisons among the lines are proposed. These 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 24 or less.

• Journal of the Korean Statistical Society
• /
• v.34 no.2
• /
• pp.141-151
• /
• 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.

• Proceedings of the Korean Society for Quality Management Conference
• /
• 1998.11a
• /
• pp.253-258
• /
• 1998

Staggered nested designs are the most popular class of unbalanced nested designs in practical fields. The most important features of the staggered nested design are that it has a very simple open-ended structure and each sum of squares in the analysis of variance has almost the same degrees of freedom. Based on the features, a class of unbalanced nested designs which is generalized of the staggered nested design is proposed. Some of the generalized staggered nested designs are shown to be more efficient than the staggered nested design in estimating some of variance components and their linear combinations.

• Journal of the Korean Data and Information Science Society
• /
• v.13 no.2
• /
• pp.175-184
• /
• 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
• /
• v.9 no.1
• /
• pp.53-61
• /
• 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.

• Communications for Statistical Applications and Methods
• /
• v.13 no.1
• /
• pp.135-140
• /
• 2006

The paper by Paik (1985) introduced a structural property of the designs which was related to the concordance matrix $NN^{t}$ of the design. This special property was termed Property-C. The designs which have Property-C need not calculation of the generalize inverse of C matrix for solution of reduced normal equation. Paik also mentioned that some block designs belong to Property-C. This paper show the Extended Group Divisible designs defined by Hinkelmann (1964) are included in Property-C.

• Journal of the Korean Statistical Society
• /
• v.15 no.2
• /
• pp.127-130
• /
• 1986

Constantine(1981) extended the results of Takeuchi(1961) by adding some new blocks to certain known E-optimal block design. But they are confined to equal blocksize designs. In this paper we agin generalize them to different blocksize case. By augmenting some known E-optimal block designs having blocks of equalsize with blocks of different sizes, additional E-optimal block designs are obtained.

• Journal of the Korean Society of Clothing and Textiles
• /
• v.11 no.3 s.25
• /
• pp.1-14
• /
• 1987

The purpose of this study was to compare with the Persian texile design having an out-standing skill in fertile designs with the Byzantine textile dosing being influenced a lot by Christinity and many Oriental factors including Hellenism. These two textile design have some similarities and differences in their patterns. The results of the study were as follows: Similarities ; 1. The Persian traditional animals, hunting scenes and cavaliers are used as the major subject in both patterns. 2. Decorative designs enclosed circular are used in both patterns. Differences ; 1. The Persian textile designs are based on Zoroasterianism, and their animal designs have the Zoroasterian religious meanings. While the Byzantine designs are affected by the Christianity. In the Byantine textile designs, the mythical subjects from ancient Rome and Greece, and the circus scenes are dominent. 3. The Persian textile designs are combative, momentary, dignifed, and realistic pattern, while the Byzantin textile designs are playful, sketchy, humouristic, and evasive pattern. 4. Vivid color effect was found in the Persian textile patterns: however, more refined and gorgeous color was used by the Byzantine textile patterns. Thus, the Persian and the Byzantine textile patterns have interrelations with each other. In general, the Persian textile patterns have affected a great deal on the Byzantine textine textile patterns. They are essentially corelated with each other, but each of them has its own characteristics.