• Journal of the Korean Statistical Society
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• v.23 no.1
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• pp.103-114
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• 1994

For a $2 \times 2$ factorial design without the restriction of a linear model or without regard to error terms having homoscedasticity, under the null hypothesis of no interaction we can have the rank transformed F statistic for interaction converge in distribution to a chi-squared random variable with one degree of random if and only if there is only main effect.

• Journal of Life Science
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• v.18 no.9
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• pp.1284-1289
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• 2008

This research was conducted to elucidate the optimum conditions for the maesil vinegar fermentation by Acetobacter sp. SK-7 using evolutionary operation (EVOP)-factorial design technique. The acidity of maesil vinegar was effected by ethanol concentration in the range of 3-7% (r=-0.5166), and glucose concentration in the range of 0.1-0.5% (r=-0.5061). The acidity of maesil vinegar was not effected by differentiation of temperature in the range of 24-$33^{\circ}C$ (r=0.1082). The optimum maesil vinegar fermentation by Acetobacter sp. SK-7 as determined by the EVOP-factorial design technique was obtained at an fermentation temperature of $30^{\circ}C$, ethanol concentration of 4%, glucose concentration of 0.2%. Furthermore, the acidity of vinegar increase from an initial acidity of 5.4% to 6.365% in the third set that is nearly 1.0% by EVOP-factorial design technique

• Journal of Microbiology and Biotechnology
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• v.17 no.11
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• pp.1880-1884
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• 2007

This study was conducted to find the optimum extraction condition of Gold-Thread for antibacterial activity against Streptococcus mutans using The evolutionary operation-factorial design technique. Higher antibacterial activity was achieved in a higher extraction temperature ($R^2=-0.79$) and in a longer extraction time ($R^2=-0.71$). Antibacterial activity was not affected by differentiation of the ethanol concentration in the extraction solvent ($R^2=-0.12$). The maximum antibacterial activity of clove against S. mutans determined by the EVOP-factorial technique was obtained at $80^{\circ}C$ extraction temperature, 26 h extraction time, and 50% ethanol concentration. The population of S. mutans decreased from 6.110 logCFU/ml in the initial set to 4.125 logCFU/ml in the third set.

• Food Science and Biotechnology
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• v.17 no.5
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• pp.899-903
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• 2008

This study was conducted in order to elucidate the optimum conditions for the extraction of clove that can be used to elicit antibacterial activity against Streptococcus mutans using the evolutionary operation (EVOP)-factorial design technique. Higher antibacterial activity was achieved in a higher extraction temperature of $80^{\circ}C$ ($r=0.7983^{**}$) and in a longer extraction time of 26 hr ($r=0.6867^*$). Antibacterial activity was not effected by differentiation of ethanol concentration in the extraction solvent (r=-0.0683). The maximum antibacterial activity of clove against S. mutans as determined by the EVOP-factorial design technique was obtained at an extraction temperature of $80^{\circ}C$, an extraction time of 26 hr and a 50% ethanol concentration. Furthermore, the population of S. mutans decreased from an initial concentration of 6.850 to 4.195 log CFU/mL in the third set that is more than 2.6 log cycles by EVOP-factorial design technique.

• 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 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 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.

• International Journal of Fluid Machinery and Systems
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• v.2 no.2
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• pp.172-178
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• 2009

This paper reports on an investigation (using RSM with commercial CFD software) of the performance characteristics of the impeller in a centrifugal pump. Geometric parameters of vane plane development were defined with the meridional shape and frontal view of the impeller. The parameters are focused on the blade-angle distributions through the impeller in a fixed meridional geometry. For screening, a $2^k$ factorial design has been used to identify the important design parameters. The objective functions are defined as the total head rise and the total efficiency at the design flow-rate. From the $2^k$ factorial design results, it is found that the incidence angles and the exit blade angle are the most important parameters influencing the performance of the pump.

• Journal of the Korea Concrete Institute
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• v.16 no.2 s.80
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• pp.269-275
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• 2004

Factorial design method is applied to investigate the effects of various factors simultaneously rather than to conduct a series of single-factor experiment. As the results, frost resistance of the concrete specimens, in both W/C ratio of 0.28 and 0.35, was highly affected by the type of coarse aggregate that is, andesite produced more durable concrete than the limestone. Durability factor of the specimens, with W/C ratio of 0.28, which were demolded after I day and transferred to the curing room was higher than those demolded after 2 days. This stated the efficiency of the high early curing in high strength concrete.

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.483-495
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• 2007

In a general fractional factorial design, the n-levels of a factor are coded by the $n^{th}$ roots of the unity. Pistone and Rogantin (2007) gave a full generalization to mixed-level designs of the theory of the polynomial indicator function using this device. This article discusses the optimal blocking scheme for nonregular designs. According to hierarchical principle, the minimum aberration (MA) has been used as an important criterion for selecting blocked regular fractional factorial designs. MA criterion is mainly based on the defining contrast groups, which only exist for regular designs but not for nonregular designs. Recently, Cheng et al. (2004) adapted the generalized (G)-MA criterion discussed by Tang and Deng (1999) in studying $2^p$ optimal blocking scheme for nonregular factorial designs. The approach is based on the method of replacement by assigning $2^p$ blocks the distinct level combinations in the column with different blocks. However, when blocking level is not a power of two, we have no clue yet in any sense. As an example, suppose we experiment during 3 days for 12-run Plackett-Burman design. How can we arrange the 12-runs into the three blocks? To solve the problem, we apply G-MA criterion to nonregular mixed-level blocked scheme via the mixed-level indicator function and give an answer for the question.