• 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 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.

• Journal of the Korean Statistical Society
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• 제36권3호
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• pp.373-386
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• 2007

In this paper, a review on second order slope rotatable designs (SOSRD) is studied. Further, different methods of constructions of SOSRD like slope rotatable central composite designs (SRCCD), SOSRD using balanced incomplete block designs (BIBD), SOSRD using pairwise balanced designs (PBD), SOSRD using partially balanced incomplete block type designs (PBIBD) and SOSRD using symmetrical unequal block arrangements (SUBA) with two unequal block sizes are examined in detail. A table is provided where for a range of different values of v (v stands for number of factors) the design points needed by different methods are compared. The optimum SOSRD with minimum number of design points for each factor is suggested for $2{\leq}v{\leq}16$.

• Journal of the Korean Statistical Society
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• 제31권2호
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• pp.153-161
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• 2002

A new method of construction of second order slope rotatable designs (SOSRD) using symmetrical unequal block arrangements (SUBA) with two unequal block sizes is suggested. The proposed method may sometimes lead to designs with less number of design points than those available in the literature. Further, bounds for the parameters of SOSRD are also obtained.

• Journal of the Korean Statistical Society
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• 제36권1호
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• pp.157-173
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• 2007

In this article it is considered that how the slope-rotatability property of a second order design for response surface model is affected by block effects and how the design points are assigned into the blocks so that the blocked design may have the property of slope-rotatability. If an unblocked design is blocked properly, it could be a slope-rotatable design with block effects and this property is named as block slope-rotatability. We approach this problem from the moment matrix of the blocked design, which plays an important role to get the variances of the estimates, and suggest conditions of block slope-rotatability.

• Journal of the Korean Statistical Society
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• 제11권1호
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• pp.36-44
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• 1982

A new design concept, called axis-slope-rotatability, is presented for the design of experiments with mixtures. This is an analogue of the Box-Hunter (1957) rotatability for second order response surface designs. By choice of design, it is possible to make the variance of the estimated slopes along the component axes constant for all axial points equidistant from the center point of the factor space. This property is called axis-slope-rotatability for mixture experiments. When the Scheffe's second degree polynomial is used, it is shown that some symmetry conditions are sufficient for axis-slope-rotatability. Several designs having this property are illustrated.

• 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.

• Journal of the Korean Statistical Society
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• 제17권2호
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• pp.121-133
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• 1988

In this paper a class of mixture designs for estimating the slope of second order Scheffe polynomial response surfaces for mixture experiments with q components is presented. The variance of the estimated directional slope at a point is a function of the direction of the slope and the design. If the variance is averaged over all possible directions in the (q-1)-dimensional simplex, 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 centroid point. This property is called "slope-rotatability over al directions in the simplex", and the necessary and sufficient conditions for mixture design to have this property are given and proved. The class of designs with this property is compared with other mixture designs and discussed.discussed.

• Journal of the Korean Statistical Society
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• 제24권2호
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• pp.519-536
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• 1995

In the design of experiments for response surface analysis, sometimes it is of interest to estimate the difference of responses at two points. If differences at points close together are involved, the design that reliably estimates the slope of response surface is important. This idea was conceptualized by slope rotatability by Hader & Park (1978) and Park (1987). Until now, second order polynomial models were only studied for slope ratatability. In this paper, we will propose the necessary and sufficient conditions for slope rotatability over all directions for the thired order polynomial models in two, three and four independent variables. Also practical slope rotatable designs over all directions for two independent variables are suggested.