• Journal of the Korean Statistical Society
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• 제34권2호
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• pp.153-160
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• 2005

In this paper, modified second order slope rotatable designs are introduced and modified slope rotatable central composite designs (SRCCD) are constructed for $2 {\le} v {\le} 17$ (v: the number of factors). Further, it can be shown for certain values of 'v', the modified SRCCD can be viewed as SRCCD constructed as with the technique of augmentation of second order rotatable design (SORD) using central composite design to SRCCD. These designs are useful in parts to estimate responses and slopes with spherical variance functions.

• Journal of Korean Society for Atmospheric Environment
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• 제24권E2호
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• pp.83-91
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• 2008

This work investigated the methodology to simultaneously optimize the ozone and relative humidity composition for the $NO_x$ degradation using soil biofilter. Experiments were made as a function of inlet ozone concentration ($0{\sim}1,770\;ppb$) and relative humidity ($38{\sim}81%$). Factorial design ($2^2+3$) and response surface methodology by central composite designs were used to examine the role of two factors and optimal response condition on $NO_x$ degradation. It was found that a second-order response surface model can properly interpret the experimental data with an $R^2$-value of 0.9730 and F-value of 71.83, based on which the maximum $NO_x$ degradation was predicted up to 92.8% within our experimental conditions.

• 품질경영학회지
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• 제40권4호
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• pp.431-440
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• 2012

Purpose: In this paper we propose modified Notz designs which are useful to experimenters who want to adopt the sequential experimentation strategy and to estimate second-order regression model with as few experimental points as possible. Methods: We first present the design matrices and design points in two or three dimensional spaces for such small sized second-order designs as small composite, hybrid, and Notz designs. Modified Notz designs are proposed and compared with some response surface designs in terms of the total number of experimental points, the estimation capability criteria such as D- and A-optimality. Results: When sequential experimentation is necessary, the modified Notz designs are recommendable. Conclusion: The result of this paper will be beneficial to experimenters who need to do experiments more efficiently, especially for those who want to reduce the time of experimentation as much as possible to develop cutting-edge products.

• Journal of the Korean Statistical Society
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• 제32권4호
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• pp.337-357
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• 2003

This paper introduces new measures for the stability of slope estimation on the second order response surface at a point and on a sphere. As a measure of point stability of slope estimation, we suggest a point dispersion measure of slope variances over all directions at a point. A spherical dispersion measure is also proposed as a measure of spherical stability of slope estimation on each sphere. Some designs are studied to explore the usefulness of the proposed measures. Using the point dispersion measure, another concept of slope rotatability called equally-stable slope rotatability is proposed as a useful property of response surface designs. We provide a set of conditions for a design to have equally-stable slope rotatability.

• 품질경영학회지
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• 제14권1호
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• pp.26-32
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• 1986

A class of multi-factor designs for estimating the slope of second order response surfaces is presented. For multi-factor designs the variance of the estimated slope at a point is a function of the direction of measurement of the slope and the design. If we average the variance over all possible directions, the averaged variance is only a function of the point and the design. By choice of design, it is possible to make this variance constant for all points equidistant from the design origin. This property is called "slope-rotatability over all directions", and the necessary and sufficient conditions for a design to have this property are given and proved. The class of design with this property is mainly discussed.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 1998년도 The 12th Asia Quality Management Symposium* Total Quality Management for Restoring Competitiveness
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• pp.580-593
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• 1998

2차 반응표면분석을 위한 부분합성계획은 실험 비용이 많이 들거나, 실험 자체가 어려워서 시간의 소비가 많은 경우, 실험오차의 독립추정이 가능할 때 효과적이다. 반응표면분석에서는 회전성과 기울기 회전성을 만족하는 것이 중요하다. 따라서 본 논문에서는 회전성과 기울기 회전성의 관점에서 부분합성계획을 살펴보고 또한 인자의 수와 중심점의 수가 변함에 따라서 어떤 a(중심에서 축점까지의 거리)의 값이 최적의 실험계획이 되도록 하는지를 연구하였다.

• 산업식품공학
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• 제15권2호
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• pp.97-115
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• 2011

이 총설에서는 반응표면분석법을 이용하여 식품제조프로세스를 최적화하는 방법에 대하여 검토하였다. 반응표면분석을 수행하기 위한 절차와 반응표면분석의 필수적인 기본이론을 설명하였고, 반응표면분석법 중에서도 대부분 사용되는 2차 실험계획법(3인자 완전요인, 중심합성, Box-Behnken, 및 Doehlert 계획법)들에 대한 장단점 및 효율성을 비교하였다. 식품제조프로세스를 최적화하는데 반응표면분석법을 적용하기 위해서는 우선 실험계획을 선택하고, 적절한 모델함수를 적합화한 다음, 적합화된 모델의 질 및 실험데이터와의 예측의 정확성을 평가할 필요가 있다. 식품제조프로세스를 최적화할 때 일부요인계획, 완전요인계획 및 Plackett-Burman 계획 등과 같은 실험계획법을 사용하여 중요한 실험인자를 일차적으로 스크린한 다음, 2차 실험계획법을 선택하는 것이 바람직하다. 실제적으로 최적실험조건을 찾기 위해서는 F-test, 수정 $R^2$ 등과 같은 분산분석을 사용하여 모델을 적합화하는 것이 바람직하다. Doehlert 계획과 Box-Behnken 계획은 중심합성계획법보다 좀 더 효율적이며, 최근에는 이 계획들을 적용한 문헌의 수가 증가하고 있는 추세이다. 더욱이 이 계획들은 3수준 완전요인계획법보다는 비교할 필요도 없이 훨씬 더 효율적이다. Box-Behnken설계는 식품분야에서와 같이 극한조건(즉, 인자들이 동시에 가장 높거나 혹은 가장 낮은 수준의 실험 조건)하에서 실험을 하는 것을 피하고자 할 때 유용하다. Doehlert 계획에서는 각 인자들의 수준(level)이 다르기 때문에, 몇몇 인자들이 가격적인 면에서 그리고(혹은) 장비사용에 제약을 받는 제한이 있다든지 혹은 인자의 중요도에 따라 수준의 수를 조절해야 할 필요가 있을 때에는 Doehlert 계획이 아주 유용하다. 종래에는 반응표면분석법의 2차 회귀모델 실험계획법 중에서 다른 계획법(Box-Behnken 계획 및 Doehlert 계획)에 비해 중심합성계획법을 압도적으로 많이 적용해 왔다. 그러나 Box-Behnken 계획 및 Doehlert 계획은 중심합성계획법보다 장점이 많기 때문에, 향후에는 Doehlert 계획과 Box-Behnken 계획을 사용하여 식품제조프로세스를 최적화하는 쪽으로 초점이 맞추어 지리라고 전망한다.

• 호남수학학술지
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• 제6권1호
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• pp.45-58
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• 1984

• 품질경영학회지
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• 제47권3호
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• pp.523-535
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• 2019

Purpose: We research on the efficient response surface methodology(RSM) design to develop a design space in Quality by Design(QbD). We propose practical designs for the successful construction of the design space in QbD by allowing different number of replicates at the box points, star points, and the center point in the rotatable central composite design(CCD). Methods: The fraction of design space(FDS) plot is used to compare designs efficiency. The FDS plot shows the fraction of the design space over which the relative standard error of predicted mean response lies below a given value. We search for practical designs whose minimal half-width of the tolerance interval per a standard deviation is less than 4.5 at 0.8 fraction of the design space. Results: The practical designs for the number of factors between two and five are listed. One of the designs in the list could be chosen depending on the experimental budget restriction. Conclusion: The designs with box points replications are more efficient than those with the star points replication. The sequential method to establish a design space is illustrated with the simulated data based on the two examples in RSM.

• Journal of the Korean Statistical Society
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• 제35권2호
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• pp.179-192
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• 2006

In this paper, a new method of modified second order slope rotatable designs (SOSRD) using balanced incomplete block designs (BIBD) for $4{\le}v{\le}16$ is presented. In this method the number of design points required is in some cases less than the number required in Victorbabu (2305) modified slope rotatable central composite designs. Further, a new method of construction of three level modified SOSRD using BIBD is presented. The modified SOSRD can be viewed as SOSRD constructed with the technique of augmentation of second order rotatable design (SORD) using BIBD to SOSRD. These designs are useful in parts to estimate responses and slopes with spherical variance functions.