• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.759-766
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• 2000

In order to design fractional factorial experiments which include some debarred combinations, we should select defining contrasts so that those combinations are to be excluded. Choi(1999) presented a method of selectign defining contrasts to construct orthogonal 3-level fractional factorial experiments which exclude some debarred combinations. In this paper, we extend Choi's method to general p-level fractional factorial experiments to select defining contrasts which cold exclude some debarred combinations.

• 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.

• 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.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.695-706
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• 1999

When fractional factorial experiments contain some infeasible treatment combinations called debarred combinations we should construct experimental designs so that those debarred combinations are to be excluded by selecting defining contrasts appropriately. By applying Franklin(1995)'s procedure for selecting defining contrasts to Cheng and Li(1993)'s method this paper presents a method of selecting defining contrasts to construct orthogonal 3-level fractional factorial experiments which exclude some debarred combinations.

• 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.

• Journal of Power System Engineering
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• v.22 no.1
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• pp.5-10
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• 2018

In order to employ factorial design on electronically-controlled diesel engine, effects of 5 factors on specific fuel consumption, nitrogen oxides and carbon monoxide were examined by fractional and full factorial design in this research. There were different results between fractional and full factorial design, then effect of variables as ambient condition and measurement of fuel consumption were confirmed. It was shown that ambient condition affected uniformly trend of nitrogen oxides and carbon monoxide. However, both ambient condition and measurement of fuel consumption had nothing to do with trend of specific fuel consumption and therefore it must be careful to employ factorial design on specific fuel consumption as response.

• 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.

• The Korean Journal of Applied Statistics
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• v.11 no.2
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• pp.303-315
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• 1998

In a factorial experiment, certain combinations of factor levels clay not be ruled out for operational or economical reason. A fractional factorial design that contains such infeasible combinations, called debarred combinations, becomes too unbalanced to estimate the required effects. This thesis presents a method of selecting defining contrasts for constructing regular $3^{n-p}$ fractional factorial design which does not contain a debarred combination. Consequently, the construction of the design is accomplished by choosing the defining contrasts so that one of defining contrasts is compatible with a debarred combination.

• 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.