• Title, Summary, Keyword: Central Composite Design

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Extended Central Composite Designs with the Axial Points Indicated by Two Numbers

  • Kim, Hyuk-Joo
    • 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.

MODIFIED SLOPE ROTATABLE CENTRAL COMPOSITE DESIGNS

  • VICTOR BABU B. RE.
    • 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.

On modified slope rotatability of central composite designs with two axial values (두 개의 축값을 갖는 중심합성설계의 수정기울기회전성에 관하여)

  • Kim, Hyuk Joo
    • 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.

A Study on the Influence of a Missing Cell in a Class of Central Composite Designs

  • Park, Sung-Hyun;Noh, Hyun-Gon
    • 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.

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Approximate Multi-Objective Optimization of Scroll Compressor Lower Frame Considering the Axial Load (축하중을 고려한 스크롤 압축기 하부 프레임의 최적설계)

  • Kim, JungHwan;Lee, Jongsoo
    • Journal of The Korean Society of Manufacturing Technology Engineers
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    • v.24 no.3
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    • pp.308-313
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    • 2015
  • In this research, a multi-objective optimal design of a scroll compressor lower frame was approximated, and the design parameters of the lower frame were selected. The sensitivity of the design parameters was induced through a parameter analysis, and the thickness was determined to be the most sensitive parameter to stress and deflection. All of the design parameters regarding the mass are sensitive factors. It was formulated for the problem about stress and deflection to be caused by the axial load. The sensitivity of the design variables was determined using an orthogonal array for the parameter analysis. Using the central composite and D-optimal designs, a second polynomial approximation of the objective and constraint functions was formulated and the accuracy was verified through an R-square. These functions were applied to the optimal design program (NSGA-II). Through a CAE analysis, the effectiveness of the central composite and D-optimal designs was determined.

Application of the Central Composite Design and Response Surface Methodology to the Treatment of Dye Using Electrochemical Oxidation (전기화학적 산화를 이용한 염료 처리에 중심합성설계와 반응표면분석법의 적용)

  • Kim, Dong-Seog;Park, Young-Seek
    • 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%).

Tensile Failure and Buckling Load Improvement of Composite Plates With A Central Hole (원공이 있는 복합재료 평판의 인장파단 및 좌굴 하중 개선)

  • 이호형
    • Proceedings of the Korean Society For Composite Materials Conference
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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.

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Development of Medium for Griseofulvin Production: Part II. Optimization of Medium Constituents Using Central Composite Design

  • Dasu, Venkata;Panda, V.T.;Chidambaram, M.
    • 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.

Ethanolysis of Soybean Oil into Biodiesel : Process Optimization via Central Composite Design

  • Tippayawong Nakorn;Kongjareon Eaksit;Jompakdee Wasan
    • Journal of Mechanical Science and Technology
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    • v.19 no.10
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    • pp.1902-1909
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    • 2005
  • A process for production of ethyl ester for use as biodiesel has been studied. The sodium hydroxide catalyzed transesterification of soybean oil with ethanol was carried out at different molar ratio of alcohol to oil, reaction temperature and catalyst amount for a constant agitation in two hours of reaction time. Central composite design and response surface methodology were used to determine optimum condition for producing biodiesel. It was found that ethanol to oil ratio and catalyst concentration have a positive influence on ester conversion as well as interaction effects between the three factors considered. An empirical model obtained was able to predict conversion as a function of ethanol to oil molar ratio, reaction temperature and catalyst concentration adequately. Optimum condition for soybean ethyl ester production was found to be moderate ethanol to oil ratio (10.5: 1), mild temperature range ($70^{\circ}C$) and high catalyst concentrations ($1.0\%$wt), with corresponding ester conversion of $93.0\%$.