• Journal of the Korean Statistical Society
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• v.34 no.2
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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.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.595-605
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• 2002

The central composite design is widely used for estimating second order response surfaces. This type of design is composed of $2^k$ factorial points, axial points and center points. In this paper, we suggest a version of central composite design where the positions of the axial points are indicated by two numbers, and study properties of this design. We obtain the variances and covariances of the estimators of the regression coefficients. Conditions are obtained for this design to be orthogonal and rotatable. This design is compared with other designs on the basis of efficiency.

• The Korean Journal of Applied Statistics
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• v.32 no.6
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• pp.867-878
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• 2019

In this paper, we applied modified slope rotatability introduced by Victorbabu (2005) to the central composite design of second type, and studied related content. We suggested methods of constructing central composite designs of second type which have modified slope rotatability. Especially, this property has the advantage that it can be used to sequential experiments, because we can obtain central composite designs of second type which have modified slope rotatability by adding experimental points without changing the axial values to central composite designs of second type having Box-Hunter rotatability. We explained central composite designs of second type which have modified slope rotatability by using two examples.

• Journal of the Korean Statistical Society
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• v.27 no.1
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• pp.133-152
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• 1998

The central composite design is widely used in the response surface analysis, because it can fit the second order model with small experimental points. In practice, the experimental data are not always obtained on all the points. When there are missing observations, many problems due to the missing cells can occur. In this paper, the influence of a missing cell on the central composite design is discussed. First, the influences of a missing cell on the variances of estimated regression coefficents are compared as $\alpha$ varies. Second, how the average predition variance is affected by a missing sell is discussed. And the influence on rotatability is investigated. Third, the influence of a missing cell on optimality, especially on D-optimality and A-optimality, is examined.

• Journal of Environmental Science International
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• v.18 no.11
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• pp.1225-1234
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• 2009

The aim of this research was to apply experimental design methodology in the optimization condition of electrochemical oxidation of Rhodamine B(RhB). The reactions of electrochemical oxidation were mathematically described as a function of parameters amounts of current, NaCl dosage, pH and time being modeled by the use of the central composite design, which was used for fitting quadratic response surface model. The application of response surface methodology using central composite design(CCD) technique yielded the following regression equation, which is an empirical relationship between the removal efficiency of RhB and test variable in actual variables: RhB removal (%) = 3.977 + 23.279$\cdot$Current + 49.124$\cdot$NaCI - 5.539$\cdot$pH - 8.863$\cdot$time - 22.710$\cdot$Current$\cdot$NaCl + 5.409$\cdot$Current$\cdot$time + 2.390$\cdot$NaCl$\cdot$time + 1.061$\cdot$pH$\cdot$time - $0.570{\cdot}time^2$. The model predicted also agree with the experimentally observed result($R^2$ = 91.9%).

• Journal of Korean Society for Quality Management
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• v.49 no.1
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• pp.31-45
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• 2021

Purpose: A noncentral composite design method is to be developed to explore farther region for the first factorial design. A general guideline for sequential experimentation is provided. Methods: (1) A non-overlapping noncentral composite design (NNCD) is developed, in which the second factorial design shares one design point that indicates the best response value in the first factorial design. (2) Four composite designs are compared in terms of the four design evaluation criteria, which are D-, A, G, and I-optimality. (3) A follow-up design strategy is suggested based on the interaction effect, direction of improvement, number of factors. Results: (1) NNCD and model building method are presented, which is useful for exploring farther region from first factorial design block. (2) The performances of the four composite designs are compared. (3) A follow-up design strategy is suggested. Conclusion: (1) NNCD will be useful to explore farther region for the first factorial design. (2) A follow-up design strategy can be beneficial to the experimental practitioners for product and process design and improvement.

• Proceedings of the Korean Society of Applied Entomolohy Conference
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• 2005.05a
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• pp.166-166
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• 2005

• Proceedings of the Korean Society For Composite Materials Conference
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• 1999.11a
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• pp.242-245
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• 1999

In aerospace industry improvement of structural performance of flight structure without increasing weight has great advantage. In this study, an innovative design method to increase the buckling load and tension failure load at the same time without increasing the weight was investigated by using the curvilinear fiber format in composite plates with central hole. It was investigated how much gain can be obtained with curvilinear fiber format for the plates with different hole size and different stacking sequence.

• Journal of Microbiology and Biotechnology
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• v.12 no.3
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• pp.360-366
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• 2002

Central composite experimental design was employed to determine the optimal concentration of medium constituents for griseofulvin production by Penicillium griseofulvum MTCC 1898 and Penicillium griseofulvum MTCC 2004. The optimal concentration of sucrose, $K_2HPO_4,\;NaNO_3,\;and\;FeSO_4{\cdot}7H_2O$ were found to be 48.08 g/1, 1.228 g/1 , 2.7 g/1, and 0.011 g/1, respectively, for Penicillium griseofulvum MTCC 1898, and for Penicillium griseofulvum MTCC 2004, 23.52 g/1, 43.67 g/1, and 0.0434 g/1 of glucose, lactose, and $MnSO_4{\cdot}H_2O$, respectively. The yield of griseofulvin under optimal composition of medium constituents increased by 1.26 and 1.38 times than prior to optimization, for Penicillium griseofulvum MTCC 1898 and Penicillium griseofulvutn MTCC 2004, respectively.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.34 no.1
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• pp.60-73
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• 1989

Two field experiments were carried out to assess the applicability of a central composite design (CCD) in determining optimum culture condition of an early rice cultivar, Unbongbyeo in southern Korea. A central composite design with two replicates was applied to five levels of five factors such as the number of hills per 3.3m2, the number of seedlings per hill, the levels of nitrogen, the transplanting date and the seedling age (Experiment 1). The levels of planting density were ranged from 30 hills to 150 hills per 3.3m2 ; the number of seedlings per hill from 1 seedling to 9 seedlings per hill; the levels of nitrogen application from 1 kg/l0a to 21 kg/l0a; the transplanting date from June 15 to July 5; the seedling age from 25 days to 45 days. A fractional factorial design was applied to three levels of five factors tested in CCD (Experiment 2). Yield per hill and per unit area were examined and the results obtained from both experiments were compared. The benefits from the central composite design were discussed. Maximum yield of brown rice per unit area was obtained at the combination of the central levels of one of five factors when the other four factors were fixed at central point. Furthermore, brown rice yield per unit area affected by interaction of two factors was maximized at the central point when the remain three factors being fixed at the central level. The responses of five factors to brown rice yield per hill and unit area were found to be a saddle point in both designs. Actual values of the stationary points were 107 hills per 3.3 m2, 4 seedlings per hill, 10 kg nitrogen per l0a, transplanting date of rice on June 26 and 33 days of seedling age in the central composite design. Brown rice yield per unit area at the stationary points were estimated 439 kg/l0a in the central composite design and 442 kg/l0a in the fractional factorial design. Considering the number of experimental treatment combinations, the central composite design was rather convenient in reducing the number of treatment combinations for similar information. It was more convenient for an experimenter to present the results from the central composite design than those from the fractional factorial design. Considering the optimum yields of brown rice per unit area at the stationary points being verified as saddle points in both designs. inter-heterogeneity of each of the factors should be avoided in setting up factors in pursuit of inducing unidirectional response of the factors to yield. Even though both the lower and higher levels in the central composite design being beyond the region of an experimenter's interest. they were considered highly valued in interpretation of the results. Conclusively. the central composite design was found to be more beneficial to optimize culture condition of paddy rice even with several levels of various factors were involved.