• 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.

• Laser Solutions
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• v.4 no.1
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• pp.29-38
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• 2001

This work was carried out to investigate the welding behavior of thin A3003 Al alloy sheets by Nd : YAG laser beam. Considering bead shape and mechanical properties, the laser pulse shapes selected were two kinds of 2-division and 3-division by varying power level and pulse duration. In order to obtain optimum conditions, the factorial design method and central composite design method were applied. Tensile test, optical microscopy, micro hardness test and TEM analysis were performed. Due to the annealing caused by thermal effect during laser welding, precipitates were coarsended. The HAZ was softened and failed during tensile test. The hardness of HAZ was lower than that of base metal, since the heat input relieved the work hardening effect and caused grain growth.

• Geomechanics and Engineering
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• v.21 no.6
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• pp.513-525
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• 2020

Slopes stabilised with piles are seldom analysed considering uncertainties in the parameters of the pile-slope system. Reliability analysis of the pile-slope system quantifies the degree of uncertainties and evaluates the safety of the system. In the present study, the reliability analysis of a slope stabilised with piles is performed using the first-order reliability method (FORM) based on Hasofer-Lind approach. The implicit performance function associated with the factor of safety (FS) of the slope is approximated using the response surface method. The analyses are carried out considering the design matrices formulated based on both the 2^k factorial design augmented with a centre run (2^k fact-centred design) and face-centered cube design (FCD). The finite element method is used as the deterministic model to compute the FS of the pile-slope system. Results are compared with the results of the Monte Carlo simulation. It is observed that the optimum location of the row of piles is at the middle of the slope to achieve the maximum FS. The results show that the reliability of the system is not uniform for different pile configurations, even if the system deterministically satisfies the target factor of safety (FS_t) criterion. The FS_t should be selected judiciously as it is observed that the reliability of the system changes drastically with the FS_t level. The results of the 2^k fact-centred design and FCD are in good agreement with each other. The procedure of the FCD is computationally costly and hence the use of 2^k fact-centred design is recommended, provided the response of the system is sufficiently linear over the factorial space.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.15 no.6
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• pp.97-102
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• 2001

This paper is concerned with optimal design of a linear DC motor which is steading fast in OA and FA systems due to simplicity in structure high-speed operation and high-precision positioning. The approach is based on the statistic method. In this study, firstly, we determine factors that affect significantly the objective function using 2-level factorial design. And then the Response Surface Methodology was app1ied to optimize these factors. Through this application design factors could be optimized within a short term and low experimental cost.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.862-865
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• 2000

The object of this paper is to evaluate the surface roughness using the experimental equation of surface roughness, which is developed in turning by an orthogonal array method. $L_9{3^4}$ orthogonal array method, one of fractional factorial design has been used to study effects of main cutting parameters such as cutting speed, feed rate and depth of cut, on the surface roughness. And the analysis of variance (ANOVA)-test has been used to check the significance of cutting parameters. Using the result of ANOVA-test, the experimental equation of surface roughness, which consists of only significant cutting parameter - feed rate, has been developed. The coefficient of determination of this equation is 0.962.

• Journal of Korean Society for Quality Management
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• v.43 no.3
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• pp.453-466
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• 2015

Purpose: The purpose of this study is to design a systematic method to estimate optimal operation conditions of design variables for an electronic device alignment system. Method: The 2-level factorial design and the central composite design are used in order to plan experiments. Based on the experiment results, a regression model is established to find optimal conditions for the design variables. Results: 3 of 5 design variables are selected as major factors that affect the alignment system significantly. The optimized condition for each variable is estimated by using a sequential experiment plan and a quadratic regression model. Conclusion: The method designed in this study provides an efficient and systematic plan to select the optimized operation condition for the design variables. The method is expected to improve inspection accuracy of the system and reduce the development cost and period.

• 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.

• Journal of Korean Institute of Industrial Engineers
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• v.39 no.5
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• pp.374-382
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• 2013

Robust design method developed by Genichi Taguchi has been very popular since the 1980s and there have been many academic and applied research works on this topic. However, college students and engineers in companies have had difficulty in understanding the method. This paper presents a procedure to implement the robust design method by an easy-to-execute paper helicopter experiment. A crossed array was adopted, which consists of a resolution IV fractional factorial design with 6 control factors and a factorial design with 3 noise factors. Three performance measures were analyzed; signal-to-noise ratio, mean, and standard deviation of the falling time of the paper helicopter that is to be maximized. Control-noise interaction plots are also given to evaluate the degree of the sensitivity of each level of the control factors to the noise factors. The procedure presented in this paper can be helpful to those who want to have basic knowledge in the robust design method.

• Laser Solutions
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• v.4 no.3
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• pp.30-39
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• 2001

This work was tamed out to apply a laser welding technique in joining between a Zn coated low carbon steel plate(SECC) and a free cutting carbon steel shaft(SUM24L) with or without W coating. Experiments were carried out and analysed by applying the FD(factorial design)method to obtain the optimum Laser welding condition. Optical microscopy, SEM, TEM and XRD analyses were performed in order to observe the microstructures in the fusion zone and the HAZ. Mechanical properties of the welded specimens were examined by microhardness test, tensile test and twist test. There was no flawed Zn in the fusion zone by EDS analysis. This means that during the welding process, Zn gas could be eliminated by appropriate shielding gas flow rate and butt welding gap. Ni coating itself did not influence on the tensile strength and hardness. However, twist bending strength and the weld depth of the Ni-coated free cutting carbon steel were lower as compared with those of the uncoated free cutting carbon steel. It was attributed to a lower absorbance of laser beam to the shin Ni surface. According to the results of the factorial design tests, the twist bending strength of welded specimens was primarily affected by pulse width, laser power, frequency and speed.

• Korean Chemical Engineering Research
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• v.46 no.4
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• pp.756-763
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• 2008

The aim of this work was to obtain uniform and well-dispersed spherical silver nanoparticles using statistical design-of-experiment methods. We performed the experiments using 2 k fractional factorial designs with respect to key factors of a general chemical reduction method. The nanoparticles prepared were characterized by SEM, TEM and UV-visible absorbance for particle size, distribution, aggregation and anisotropy. The data obtained were analyzed and optimized using a statistical software, Minitab. The design-of-experiment methods using quantified data enabled us to determine key factors and appreciate interactions between factors. The measured properties of nanoparticles were dominated not only by individual one or two main factors but also by interactions between factors. The appropriate combination of the factors produced small, narrow-distributed and non-aggregated silver nanoparticles of about 30 nm with approximately 10% standard deviation.