• 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.

• Journal of Korean Society for Quality Management
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• v.38 no.1
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• pp.42-51
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• 2010

For the fractional factorial designs, the resolution-IV designs can be used when we want to estimate the main effects and to investigate the structure of the non-negligible two-factor interaction effects, when the three-factor and higher order interaction effects are all negligible. However we need to add the additional treatment combinations in order to identify the influential interactions for the resolution-IV fractional factorial designs. In this paper we investigate the statistical structure for 3-level resolution-IV designs constructed by fold-over scheme and introduce a method for analyzing the influential two-factor interactions.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.3
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• pp.283-290
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• 2002

Two-level fractional factorial designs are widely used when many factors are considered. When two-level fractional factorial designs are used, some effects are confounded with each other. To break the confounding between effects, we can use fractional factorial designs, called fold-over designs, in which certain signs in the design generators are switched. In this paper, optimal fold-over designs with four-level quantitative and two-level factors are presented for (1) the initial designs without curvature effect and (2) those with curvature effect. Optimal fold-over design tables are provided for 8-run, 16-run, and 32-run experiments.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.353-359
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• 1998

Factorial designs with two-level factors represent the smallest factorial experiments. The system of notation and confounding and fractional factorial schemes developed for the $2^N$system are found in standard textbooks of experimental designs. Just as in the $2^N$ system, the general confounding and fractional factorial schemes are possible in $3^N,5^N$, .... , and $\rho^N$ where $\rho$ is a prime number. Hence, we have the $\rho^N$ system. In this article, the author proposes a new algorithm for constructing fractional factorial plans in the $\rho^N$ system.

• Proceedings of the Korean Society for Quality Management Conference
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• 2010.04a
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• pp.129-138
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• 2010

For the fractional factorial designs, the resolution-IV designs can be used when we want to estimate the main effects and to investigate the structure of the non-negligible two-factor interaction effects, when the three-factor and higher order interaction effects are all negligible. However we need to add the additional treatment combination in order to identify the influential interactions for the resolution-IV fracrtional factorial designs. In this paper we investigate the statistical structure for 3-level resolution-IV designs constructed by fold-over scheme and introduce a method for analyzing the influential two-factor interactions.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.277-288
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• 1996

The minimum aberration criterion is commonly used for selecting good fractional factorial designs. In this paper we give same necessary conditions for $3^{n-k}$ fractional factorial designs. We obtain minimum aberration $3^{n-k}$ designs for k = 2 and any n. For k > 2, minimum aberration designs have not found yet. As an alternative, we select a design with minimum aberration among minimum-variance designs.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.707-714
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• 2003

Because of complex aliasing, nonregular designs have traditionally been used for screening only main effects. However, complex aliasing actually may allow some interactions entertained and estimated without making additional runs. According to hierarchical principle, the minimum aberration has been used as an important criterion for selecting regular fractional factorial designs. The criterion is not applicable to nonregular designs. In this paper, we give a criterion for choosing fractional factorial designs based on the fan theory. The criterion is focused on the partial ordering given by set inclusion on estimable sets which is called leaves.

• Communications for Statistical Applications and Methods
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• v.15 no.4
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• pp.497-507
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• 2008

Confounding techniques have to be used repeatedly in the situations where it is necessary to perform only 2 runs under homogeneous conditions in $2^m$ factorial and fractional factorial experiment. Combinations of confounded $2^m$ factorial and fractional factorial designs enable the estimation of all main effects and all of or a part of 2 factor interaction effects. Defining contrast are used for our designs and treatment combinations of designs to be run are presented.

• Journal of Korean Society for Quality Management
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• v.40 no.1
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• pp.15-24
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• 2012

For the construction of fractional factorial designs, the various arrays can be widely used. In this paper we review the statistical properties of fractional designs constructed by two arrays such as orthogonal array and partially balanced array, and develop a quick and easy method for analyzing unreplicated saturated designs. The proposed method can be characterized that we control the error rate by experiment-wise way and exploit the multivariate Student $t$-distribution. Especially the proposed method can be used efficiently together with some exploratory analysis methods, such as half normal probability plot method.

• Journal of Korean Society for Quality Management
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• v.32 no.3
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• pp.234-243
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• 2004

In this paper, we study the optimality of 2-level resolution V minimal fractional factorial designs which can be constructed by using a partially balanced array. Moreover the relative efficiencies of such designs are compared in the sense of three optimality criteria such as determinant(D)-optimality, trace(A)-optimality, and eigenvalue(E) -optimality criterion.